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Theorem r19.37av 2868
Description: Restricted version of one direction of Theorem 19.37 of [Margaris] p. 90. (The other direction doesn't hold when  A is empty.) (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 1673 . 2  |-  F/ x ph
21r19.37 2867 1  |-  ( E. x  e.  A  (
ph  ->  ps )  -> 
( ph  ->  E. x  e.  A  ps )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wrex 2714
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-12 1792
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-ral 2718  df-rex 2719
This theorem is referenced by:  ssiun  4210  isucn2  19852
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