Theorem iexdeh ≪ | index | src | ≫

theorem iexdeh {x: nat} (a: nat) (G b: wff x):
  $ F/ x G $ >
  $ G /\ x = a -> b $ >
  $ G -> E. x b $;

Step	Hyp	Ref	Expression
1		ax_6	E. x x = a
2		exim	A. x (x = a -> b) -> E. x x = a -> E. x b
3		hyp h	F/ x G
4		hyp e	G /\ x = a -> b
5	4	exp	G -> x = a -> b
6	3, 5	ialdh	G -> A. x (x = a -> b)
7	2, 6	syl	G -> E. x x = a -> E. x b
8	1, 7	mpi	G -> E. 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_12)