Theorem 19.21t-1OLD 2212

Description: One direction of the bi-conditional in 19.21t 2073. Unlike the reverse implication, it does not depend on ax-10 2019. Obsolete as of 6-Oct-2021 (Contributed by Wolf Lammen, 4-Jul-2021.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
19.21t-1OLD	|- ( F/ x ph -> ( A. x ( ph -> ps ) -> ( ph -> A. x ps ) ) )

Proof of Theorem 19.21t-1OLD

Step	Hyp	Ref	Expression
1		nfrOLD 2188	. 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/wnfOLD 1709

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-nfOLD 1721

This theorem is referenced by:  19.21tOLD  2213  stdpc5OLDOLD  2217