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Theorem reximddv 23028
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 598 . . 3  |-  ( (
ph  /\  x  e.  A )  ->  ( ps  ->  ch ) )
43reximdva 2655 . 2  |-  ( ph  ->  ( E. x  e.  A  ps  ->  E. x  e.  A  ch )
)
51, 4mpd 14 1  |-  ( ph  ->  E. x  e.  A  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    e. wcel 1684   E.wrex 2544
This theorem is referenced by:  ballotlemfc0  23051  ballotlemfcc  23052
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532  df-ral 2548  df-rex 2549
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