Theorem bj-alrimhi 32604

Description: An inference associated with sylgt 1749 and bj-exlimh 32602. (Contributed by BJ, 12-May-2019.)

Hypothesis

Ref	Expression
bj-alrimhi.1	|- ( ph -> ps )

Assertion

Ref	Expression
bj-alrimhi	|- ( F/ x ph -> ( E. x ph -> A. x ps ) )

Proof of Theorem bj-alrimhi

Step	Hyp	Ref	Expression
1		df-nf 1710	. . 3 |- ( F/ x ph <-> ( E. x ph -> A. x ph ) )
2	1	biimpi 206	. 2 |- ( F/ x ph -> ( E. x ph -> A. x ph ) )
3		bj-alrimhi.1	. . 3 |- ( ph -> ps )
4	3	alimi 1739	. 2 |- ( A. x ph -> A. x ps )
5	2, 4	syl6 35	1 |- ( F/ x ph -> ( E. x ph -> A. x ps ) )

Syntax hints:   -> wi 4   A.wal 1481   E.wex 1704   F/wnf 1708

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

This theorem depends on definitions:  df-bi 197  df-nf 1710

This theorem is referenced by: (None)