Theorem ra4v 3524

Description: Version of ra4 3525 with a dv condition, requiring fewer axioms. This is stdpc5v 1867 for a restricted domain. (Contributed by BJ, 27-Mar-2020.)

Assertion

Ref	Expression
ra4v	|- ( A. x e. A ( ph -> ps ) -> ( ph -> A. x e. A ps ) )

Distinct variable group:   ph, x

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

Proof of Theorem ra4v

Step	Hyp	Ref	Expression
1		r19.21v 2960	. 2 |- ( A. x e. A ( ph -> ps ) <-> ( ph -> A. x e. A ps ) )
2	1	biimpi 206	1 |- ( A. x e. A ( ph -> ps ) -> ( ph -> A. x e. A ps ) )

Syntax hints:   -> wi 4   A.wral 2912

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-ex 1705  df-ral 2917

This theorem is referenced by:  wfr3g  7413  frr3g  31779