Theorem bj-stdpc5 32815

Description: More direct proof of stdpc5 2076. (Contributed by BJ, 15-Sep-2018.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-stdpc5.1	|- F/ x ph

Assertion

Ref	Expression
bj-stdpc5	|- ( A. x ( ph -> ps ) -> ( ph -> A. x ps ) )

Proof of Theorem bj-stdpc5

Step	Hyp	Ref	Expression
1		bj-stdpc5.1	. 2 |- F/ x ph
2		stdpc5t 32814	. 2 |- ( F/ x ph -> ( A. x ( ph -> ps ) -> ( ph -> A. x ps ) ) )
3	1, 2	ax-mp 5	1 |- ( 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: (None)