Theorem reximdd

Description: Deduction from Theorem 19.22 of Margaris p. 90. (Contributed by Glauco Siliprandi, 5-Feb-2022)

	Ref	Expression
Hypotheses	reximdd.1	|- F/ x ph
	reximdd.2	|- ( ( ph /\ x e. A /\ ps ) -> ch )
	reximdd.3	|- ( ph -> E. x e. A ps )
Assertion	reximdd	|- ( ph -> E. x e. A ch )

Proof

Step	Hyp	Ref	Expression
1		reximdd.1	|- F/ x ph
2		reximdd.2	|- ( ( ph /\ x e. A /\ ps ) -> ch )
3		reximdd.3	|- ( ph -> E. x e. A ps )
4	2	3exp	|- ( ph -> ( x e. A -> ( ps -> ch ) ) )
5	1 4	reximdai	|- ( ph -> ( E. x e. A ps -> E. x e. A ch ) )
6	3 5	mpd	|- ( ph -> E. x e. A ch )