Theorem stdpc5t 32814

Description: Closed form of stdpc5 2076. (Possible to place it before 19.21t 2073 and use it to prove 19.21t 2073). (Contributed by BJ, 15-Sep-2018.) (Proof modification is discouraged.)

Assertion

Ref	Expression
stdpc5t	|- ( F/ x ph -> ( A. x ( ph -> ps ) -> ( ph -> A. x ps ) ) )

Proof of Theorem stdpc5t

Step	Hyp	Ref	Expression
1		nf5r 2064	. 2 |- ( F/ x ph -> ( ph -> A. x ph ) )
2		alim 1738	. 2 |- ( A. x ( ph -> ps ) -> ( A. x ph -> A. x ps ) )
3	1, 2	syl9 77	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-stdpc5  32815  bj-19.21t  32817