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Theorem 19.38OLD 1895
Description: Obsolete proof of 19.38 1812 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 1747 . . 3  |-  F/ x E. x ph
2 nfa1 1806 . . 3  |-  F/ x A. x ps
31, 2nfim 1832 . 2  |-  F/ x
( E. x ph  ->  A. x ps )
4 19.8a 1762 . . 3  |-  ( ph  ->  E. x ph )
5 sp 1763 . . 3  |-  ( A. x ps  ->  ps )
64, 5imim12i 55 . 2  |-  ( ( E. x ph  ->  A. x ps )  -> 
( ph  ->  ps )
)
73, 6alrimi 1781 1  |-  ( ( E. x ph  ->  A. x ps )  ->  A. x ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1549   E.wex 1550
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-ex 1551  df-nf 1554
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