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Theorem r19.37av 3004
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 1678 . 2  |-  F/ x ph
21r19.37 3003 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 2808
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-12 1798
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1592  df-nf 1595  df-ral 2812  df-rex 2813
This theorem is referenced by:  ssiun  4360  isucn2  20510
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