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Theorem 19.37aiv 1565
Description: Inference from Theorem 19.37 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.37aiv.1  |-  E. x
( ph  ->  ps )
Assertion
Ref Expression
19.37aiv  |-  ( ph  ->  E. x ps )
Distinct variable group:    ph, x
Allowed substitution hint:    ps( x)

Proof of Theorem 19.37aiv
StepHypRef Expression
1 19.37aiv.1 . 2  |-  E. x
( ph  ->  ps )
2 nfv 1421 . . 3  |-  F/ x ph
3219.37-1 1564 . 2  |-  ( E. x ( ph  ->  ps )  ->  ( ph  ->  E. x ps )
)
41, 3ax-mp 7 1  |-  ( ph  ->  E. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1381
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427
This theorem depends on definitions:  df-bi 110  df-nf 1350
This theorem is referenced by:  eqvinc  2667  limom  4336
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