Theorem bj-alrim 32683

Description: Closed form of alrimi 2082. (Contributed by BJ, 2-May-2019.)

Assertion

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

Proof of Theorem bj-alrim

Step	Hyp	Ref	Expression
1		nf5r 2064	. 2 |- ( F/ x ph -> ( ph -> A. x ph ) )
2		sylgt 1749	. 2 |- ( A. x ( ph -> ps ) -> ( ( ph -> A. x ph ) -> ( ph -> A. x ps ) ) )
3	1, 2	syl5com 31	1 |- ( F/ x ph -> ( A. x ( ph -> ps ) -> ( ph -> A. x ps ) ) )

Syntax hints:   -> wi 4   A.wal 1481   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  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705  df-nf 1710

This theorem is referenced by:  bj-alrim2  32684