Theorem bj-ax12i

Description: A weakening of bj-ax12ig that is sufficient to prove a weak form of the axiom of substitution ax-12 . The general statement of which ax12i is an instance. (Contributed by BJ, 29-Sep-2019)

	Ref	Expression
Hypotheses	bj-ax12i.1	|- ( ph -> ( ps <-> ch ) )
	bj-ax12i.2	|- ( ch -> A. x ch )
Assertion	bj-ax12i	|- ( ph -> ( ps -> A. x ( ph -> ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		bj-ax12i.1	|- ( ph -> ( ps <-> ch ) )
2		bj-ax12i.2	|- ( ch -> A. x ch )
3	2	a1i	|- ( ph -> ( ch -> A. x ch ) )
4	1 3	bj-ax12ig	|- ( ph -> ( ps -> A. x ( ph -> ps ) ) )