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Theorem 19.38OLD 1896
Description: Obsolete proof of 19.38 1813 as of 2-Jan-2018. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
19.38OLD  |-  ( ( E. x ph  ->  A. x ps )  ->  A. x ( ph  ->  ps ) )

Proof of Theorem 19.38OLD
StepHypRef Expression
1 nfe1 1748 . . 3  |-  F/ x E. x ph
2 nfa1 1807 . . 3  |-  F/ x A. x ps
31, 2nfim 1833 . 2  |-  F/ x
( E. x ph  ->  A. x ps )
4 19.8a 1763 . . 3  |-  ( ph  ->  E. x ph )
5 sp 1764 . . 3  |-  ( A. x ps  ->  ps )
64, 5imim12i 56 . 2  |-  ( ( E. x ph  ->  A. x ps )  -> 
( ph  ->  ps )
)
73, 6alrimi 1782 1  |-  ( ( E. x ph  ->  A. x ps )  ->  A. x ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1550   E.wex 1551
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-ex 1552  df-nf 1555
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