Theorem bj-ax12wlem 32617

Description: A lemma used to prove a weak version of the axiom of substitution ax-12 2047. (Temporary comment: The general statement that ax12wlem 2009 proves.) (Contributed by BJ, 20-Mar-2020.)

Hypothesis

Ref	Expression
bj-ax12wlem.1	|- ( ph -> ( ps <-> ch ) )

Assertion

Ref	Expression
bj-ax12wlem	|- ( ph -> ( ps -> A. x ( ph -> ps ) ) )

Distinct variable group:   ch, x

Allowed substitution hints:   ph( x)   ps( x)

Proof of Theorem bj-ax12wlem

Step	Hyp	Ref	Expression
1		bj-ax12wlem.1	. 2 |- ( ph -> ( ps <-> ch ) )
2		ax-5 1839	. 2 |- ( ch -> A. x ch )
3	1, 2	bj-ax12i 32616	1 |- ( ph -> ( ps -> A. x ( ph -> ps ) ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  bj-ax12w  32665