Theorem exeqed ≪ | index | src | ≫

theorem exeqed (G: wff) {x: nat} (a: nat) (p: wff x) (q: wff):
  $ G /\ x = a -> (p <-> q) $ >
  $ G -> (E. x (x = a /\ p) <-> q) $;

Step	Hyp	Ref	Expression
1		dfsb3	[a / x] p <-> E. x (x = a /\ p)
2		hyp e	G /\ x = a -> (p <-> q)
3	2	sbed	G -> ([a / x] p <-> q)
4	1, 3	syl5bbr	G -> (E. x (x = a /\ p) <-> q)

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)