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Theorem 19.38 1822
Description: Theorem 19.38 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
19.38  |-  ( ( E. x ph  ->  A. x ps )  ->  A. x ( ph  ->  ps ) )

Proof of Theorem 19.38
StepHypRef Expression
1 nfe1 1718 . . 3  |-  F/ x E. x ph
2 nfa1 1768 . . 3  |-  F/ x A. x ps
31, 2nfim 1781 . 2  |-  F/ x
( E. x ph  ->  A. x ps )
4 19.8a 1730 . . 3  |-  ( ph  ->  E. x ph )
5 sp 1728 . . 3  |-  ( A. x ps  ->  ps )
64, 5imim12i 53 . 2  |-  ( ( E. x ph  ->  A. x ps )  -> 
( ph  ->  ps )
)
73, 6alrimi 1757 1  |-  ( ( E. x ph  ->  A. x ps )  ->  A. x ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530   E.wex 1531
This theorem is referenced by:  pm10.53  27664
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535
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