Theorem nfxab1 | index | src |

theorem nfxab1 {x: nat} (A B: set x): $ FS/ x A $ > $ FS/ x X\ x e. A, B $;
StepHypRefExpression
1 hyp h1
FS/ x A
2 1 nfel2
F/ x fst a1 e. A
3 nfsbs1
FS/ x S[fst a1 / x] B
4 3 nfel2
F/ x snd a1 e. S[fst a1 / x] B
5 2, 4 nfan
F/ x fst a1 e. A /\ snd a1 e. S[fst a1 / x] B
6 5 nfab
FS/ x {a1 | fst a1 e. A /\ snd a1 e. S[fst a1 / x] B}
7 6 conv xab
FS/ x X\ x e. A, B

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp, itru), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_11, ax_12), axs_set (elab, ax_8)