% Mizar problem: t21_card_4,card_4,225,35 
fof(t21_card_4,conjecture,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ( A = B
          <=> k2_card_1(B) = k2_card_1(A) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_card_1,cc1_ordinal1,cc2_ordinal1,d5_card_1,dt_k1_card_1,dt_k2_card_1,rc1_card_1,rc1_ordinal1,redefinition_r2_wellord2,reflexivity_r2_wellord2,symmetry_r2_wellord2,t20_card_4]),
    [file(card_4,t21_card_4)]).

fof(cc1_card_1,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(card_1,cc1_card_1),
    []).

fof(cc1_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    []).

fof(cc2_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    []).

fof(d5_card_1,axiom,(
    ! [A,B] : 
      ( v1_card_1(B)
     => ( B = k1_card_1(A)
      <=> r2_wellord2(A,B) ) ) ),
    file(card_1,d5_card_1),
    []).

fof(dt_k1_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    []).

fof(dt_k2_card_1,axiom,(
    ! [A] : v1_card_1(k2_card_1(A)) ),
    file(card_1,k2_card_1),
    []).

fof(rc1_card_1,axiom,(
    ? [A] : v1_card_1(A) ),
    file(card_1,rc1_card_1),
    []).

fof(rc1_ordinal1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    []).

fof(redefinition_r2_wellord2,axiom,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> r2_tarski(A,B) ) ),
    file(wellord2,r2_wellord2),
    []).

fof(reflexivity_r2_wellord2,axiom,(
    ! [A,B] : r2_wellord2(A,A) ),
    file(wellord2,r2_wellord2),
    []).

fof(symmetry_r2_wellord2,axiom,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
     => r2_wellord2(B,A) ) ),
    file(wellord2,r2_wellord2),
    []).

fof(t20_card_4,axiom,(
    ! [A,B] : 
      ( k1_card_1(A) = k1_card_1(B)
    <=> k2_card_1(A) = k2_card_1(B) ) ),
    file(card_4,t20_card_4),
    []).