Theorem stdpc5OLD 2077

Description: Obsolete proof of stdpc5 2076 as of 11-Oct-2021. (Contributed by NM, 22-Sep-1993.) (Revised by Mario Carneiro, 12-Oct-2016.) (Proof shortened by Wolf Lammen, 1-Jan-2018.) Remove dependency on ax-10 2019. (Revised by Wolf Lammen, 4-Jul-2021.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
stdpc5.1	|- F/ x ph

Assertion

Ref	Expression
stdpc5OLD	|- ( A. x ( ph -> ps ) -> ( ph -> A. x ps ) )

Proof of Theorem stdpc5OLD

Step	Hyp	Ref	Expression
1		stdpc5.1	. 2 |- F/ x ph
2		19.21t 2073	. . 3 |- ( F/ x ph -> ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) ) )
3	2	biimpd 219	. 2 |- ( F/ x ph -> ( A. x ( ph -> ps ) -> ( ph -> A. x ps ) ) )
4	1, 3	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)