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Theorem reximi2 2415
Description: Inference quantifying both antecedent and consequent, based on Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 8-Nov-2004.)
Hypothesis
Ref Expression
reximi2.1  |-  ( ( x  e.  A  /\  ph )  ->  ( x  e.  B  /\  ps )
)
Assertion
Ref Expression
reximi2  |-  ( E. x  e.  A  ph  ->  E. x  e.  B  ps )

Proof of Theorem reximi2
StepHypRef Expression
1 reximi2.1 . . 3  |-  ( ( x  e.  A  /\  ph )  ->  ( x  e.  B  /\  ps )
)
21eximi 1491 . 2  |-  ( E. x ( x  e.  A  /\  ph )  ->  E. x ( x  e.  B  /\  ps ) )
3 df-rex 2312 . 2  |-  ( E. x  e.  A  ph  <->  E. x ( x  e.  A  /\  ph )
)
4 df-rex 2312 . 2  |-  ( E. x  e.  B  ps  <->  E. x ( x  e.  B  /\  ps )
)
52, 3, 43imtr4i 190 1  |-  ( E. x  e.  A  ph  ->  E. x  e.  B  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 97   E.wex 1381    e. wcel 1393   E.wrex 2307
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-ial 1427
This theorem depends on definitions:  df-bi 110  df-rex 2312
This theorem is referenced by:  btwnz  8357
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