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Theorem exlimdd 1844
Description: Existential elimination rule of natural deduction. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypotheses
Ref Expression
exlimdd.1  |-  F/ x ph
exlimdd.2  |-  F/ x ch
exlimdd.3  |-  ( ph  ->  E. x ps )
exlimdd.4  |-  ( (
ph  /\  ps )  ->  ch )
Assertion
Ref Expression
exlimdd  |-  ( ph  ->  ch )

Proof of Theorem exlimdd
StepHypRef Expression
1 exlimdd.3 . 2  |-  ( ph  ->  E. x ps )
2 exlimdd.1 . . 3  |-  F/ x ph
3 exlimdd.2 . . 3  |-  F/ x ch
4 exlimdd.4 . . . 4  |-  ( (
ph  /\  ps )  ->  ch )
54ex 114 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
62, 3, 5exlimd 1576 . 2  |-  ( ph  ->  ( E. x ps 
->  ch ) )
71, 6mpd 13 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103   F/wnf 1436   E.wex 1468
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie2 1470  ax-4 1487
This theorem depends on definitions:  df-bi 116  df-nf 1437
This theorem is referenced by:  fvmptdf  5508  ovmpodf  5902  exmidfodomrlemr  7058  exmidfodomrlemrALT  7059  ltexprlemm  7415
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