Theorem nfsbid | index | src |

theorem nfsbid (G: wff) {x: nat} (A B: set x):
  $ G -> A == B $ >
  $ G -> ((FS/ x A) <-> (FS/ x B)) $;
StepHypRefExpression
1 hyp h
G -> A == B
2 1 eleq2d
G -> (y e. A <-> y e. B)
3 2 nfeqd
G -> ((F/ x y e. A) <-> (F/ x y e. B))
4 3 aleqd
G -> (A. y (F/ x y e. A) <-> A. y (F/ x y e. B))
5 4 conv nfs
G -> ((FS/ x A) <-> (FS/ x B))

Axiom use

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