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Theorem 19.36i 1820
Description: Inference from Theorem 19.36 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
19.36.1  |-  F/ x ps
19.36i.2  |-  E. x
( ph  ->  ps )
Assertion
Ref Expression
19.36i  |-  ( A. x ph  ->  ps )

Proof of Theorem 19.36i
StepHypRef Expression
1 19.36i.2 . 2  |-  E. x
( ph  ->  ps )
2 19.36.1 . . 3  |-  F/ x ps
3219.36 1819 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  ps ) )
41, 3mpbi 199 1  |-  ( A. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530   E.wex 1531   F/wnf 1534
This theorem is referenced by:  19.36aiv  1850  vtoclf  2850
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-ex 1532  df-nf 1535
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