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Theorem 19.38 1611
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 hbe1 1429 . . 3  |-  ( E. x ph  ->  A. x E. x ph )
2 hba1 1478 . . 3  |-  ( A. x ps  ->  A. x A. x ps )
31, 2hbim 1482 . 2  |-  ( ( E. x ph  ->  A. x ps )  ->  A. x ( E. x ph  ->  A. x ps )
)
4 19.8a 1527 . . 3  |-  ( ph  ->  E. x ph )
5 ax-4 1445 . . 3  |-  ( A. x ps  ->  ps )
64, 5imim12i 58 . 2  |-  ( ( E. x ph  ->  A. x ps )  -> 
( ph  ->  ps )
)
73, 6alrimih 1403 1  |-  ( ( E. x ph  ->  A. x ps )  ->  A. x ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1287   E.wex 1426
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-ial 1472  ax-i5r 1473
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  19.23t  1612  sbi2v  1820  mo3h  2001  rgenm  3384  ralm  3386
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