Theorem nfnbid | index | src |

theorem nfnbid (G: wff) {x: nat} (a b: nat x):
  $ G -> a = b $ >
  $ G -> ((FN/ x a) <-> (FN/ x b)) $;
StepHypRefExpression
1 hyp h
G -> a = b
2 1 eqeq2d
G -> (y = a <-> y = b)
3 2 nfeqd
G -> ((F/ x y = a) <-> (F/ x y = b))
4 3 aleqd
G -> (A. y (F/ x y = a) <-> A. y (F/ x y = b))
5 4 conv nfn
G -> ((FN/ x a) <-> (FN/ 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)