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Theorem stdpc5t 31340
Description: Closed form of stdpc5 1967. (Possible to place it before 19.21t 1963 and use it to prove 19.21t 1963). (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
StepHypRef Expression
1 nfr 1928 . 2  |-  ( F/ x ph  ->  ( ph  ->  A. x ph )
)
2 alim 1677 . 2  |-  ( A. x ( ph  ->  ps )  ->  ( A. x ph  ->  A. x ps ) )
31, 2syl9 73 1  |-  ( F/ x ph  ->  ( A. x ( ph  ->  ps )  ->  ( ph  ->  A. x ps )
) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435   F/wnf 1661
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-12 1909
This theorem depends on definitions:  df-bi 188  df-ex 1658  df-nf 1662
This theorem is referenced by:  bj-stdpc5  31341  bj-19.21t  31343
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