Theorem nfeqd | index | src |

theorem nfeqd (_G: wff) {x: nat} (_a1 _a2: wff x):
  $ _G -> (_a1 <-> _a2) $ >
  $ _G -> ((F/ x _a1) <-> (F/ x _a2)) $;
StepHypRefExpression
1 hyp _ah
_G -> (_a1 <-> _a2)
2 1 aleqd
_G -> (A. x _a1 <-> A. x _a2)
3 1, 2 imeqd
_G -> (_a1 -> A. x _a1 <-> _a2 -> A. x _a2)
4 3 aleqd
_G -> (A. x (_a1 -> A. x _a1) <-> A. x (_a2 -> A. x _a2))
5 4 conv nf
_G -> ((F/ x _a1) <-> (F/ x _a2))

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp), axs_pred_calc (ax_gen, ax_4, ax_5)