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Theorem r19.37av 2508
Description: Restricted version of one direction of Theorem 19.37 of [Margaris] p. 90. (Contributed by NM, 2-Apr-2004.)
Assertion
Ref Expression
r19.37av  |-  ( E. x  e.  A  (
ph  ->  ps )  -> 
( ph  ->  E. x  e.  A  ps )
)
Distinct variable group:    ph, x
Allowed substitution hints:    ps( x)    A( x)

Proof of Theorem r19.37av
StepHypRef Expression
1 nfv 1462 . 2  |-  F/ x ph
21r19.37 2507 1  |-  ( E. x  e.  A  (
ph  ->  ps )  -> 
( ph  ->  E. x  e.  A  ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wrex 2350
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  df-ral 2354  df-rex 2355
This theorem is referenced by:  ssiun  3728
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