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Theorem 19.37aiv 1606
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 1462 . . 3  |-  F/ x ph
3219.37-1 1605 . 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 1422
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 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by:  eqvinc  2719  limom  4356
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