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Theorem rexlimddv 2747
Description: Restricted existential elimination rule of natural deduction. (Contributed by Mario Carneiro, 15-Jun-2016.)
Hypotheses
Ref Expression
rexlimddv.1  |-  ( ph  ->  E. x  e.  A  ps )
rexlimddv.2  |-  ( (
ph  /\  ( x  e.  A  /\  ps )
)  ->  ch )
Assertion
Ref Expression
rexlimddv  |-  ( ph  ->  ch )
Distinct variable groups:    ph, x    ch, x
Allowed substitution hints:    ps( x)    A( x)

Proof of Theorem rexlimddv
StepHypRef Expression
1 rexlimddv.1 . 2  |-  ( ph  ->  E. x  e.  A  ps )
2 rexlimddv.2 . . 3  |-  ( (
ph  /\  ( x  e.  A  /\  ps )
)  ->  ch )
32rexlimdvaa 2744 . 2  |-  ( ph  ->  ( E. x  e.  A  ps  ->  ch ) )
41, 3mpd 14 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    e. wcel 1710   E.wrex 2620
This theorem is referenced by:  mreexexlem4d  13642  mreexdomd  13644  mtestbdd  19882  chordthm  20239  esumpcvgval  23734  lgambdd  24070  lgamucov  24071  lgamcvglem  24073  lgamcvg2  24088
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-ral 2624  df-rex 2625
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