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Theorem reximddv 2469
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by Thierry Arnoux, 7-Dec-2016.)
Hypotheses
Ref Expression
reximddva.1  |-  ( (
ph  /\  ( x  e.  A  /\  ps )
)  ->  ch )
reximddva.2  |-  ( ph  ->  E. x  e.  A  ps )
Assertion
Ref Expression
reximddv  |-  ( ph  ->  E. x  e.  A  ch )
Distinct variable group:    ph, x
Allowed substitution hints:    ps( x)    ch( x)    A( x)

Proof of Theorem reximddv
StepHypRef Expression
1 reximddva.2 . 2  |-  ( ph  ->  E. x  e.  A  ps )
2 reximddva.1 . . . 4  |-  ( (
ph  /\  ( x  e.  A  /\  ps )
)  ->  ch )
32expr 367 . . 3  |-  ( (
ph  /\  x  e.  A )  ->  ( ps  ->  ch ) )
43reximdva 2468 . 2  |-  ( ph  ->  ( E. x  e.  A  ps  ->  E. x  e.  A  ch )
)
51, 4mpd 13 1  |-  ( ph  ->  E. x  e.  A  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    e. wcel 1434   E.wrex 2354
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 2358  df-rex 2359
This theorem is referenced by:  reximddv2  2470
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