Theorem bj-ax12w

Description: The general statement that ax12w proves. (Contributed by BJ, 20-Mar-2020)

	Ref	Expression
Hypotheses	bj-ax12w.1	|- ( ph -> ( ps <-> ch ) )
	bj-ax12w.2	|- ( y = z -> ( ps <-> th ) )
Assertion	bj-ax12w	|- ( ph -> ( A. y ps -> A. x ( ph -> ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		bj-ax12w.1	|- ( ph -> ( ps <-> ch ) )
2		bj-ax12w.2	|- ( y = z -> ( ps <-> th ) )
3	2	spw	|- ( A. y ps -> ps )
4	1	bj-ax12wlem	|- ( ph -> ( ps -> A. x ( ph -> ps ) ) )
5	3 4	syl5	|- ( ph -> ( A. y ps -> A. x ( ph -> ps ) ) )