ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  rexlimdvaa Unicode version

Theorem rexlimdvaa 2434
Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by Mario Carneiro, 15-Jun-2016.)
Hypothesis
Ref Expression
rexlimdvaa.1  |-  ( (
ph  /\  ( x  e.  A  /\  ps )
)  ->  ch )
Assertion
Ref Expression
rexlimdvaa  |-  ( ph  ->  ( E. x  e.  A  ps  ->  ch ) )
Distinct variable groups:    ph, x    ch, x
Allowed substitution hints:    ps( x)    A( x)

Proof of Theorem rexlimdvaa
StepHypRef Expression
1 rexlimdvaa.1 . . 3  |-  ( (
ph  /\  ( x  e.  A  /\  ps )
)  ->  ch )
21expr 357 . 2  |-  ( (
ph  /\  x  e.  A )  ->  ( ps  ->  ch ) )
32rexlimdva 2433 1  |-  ( ph  ->  ( E. x  e.  A  ps  ->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 97    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-17 1419  ax-ial 1427  ax-i5r 1428
This theorem depends on definitions:  df-bi 110  df-nf 1350  df-ral 2311  df-rex 2312
This theorem is referenced by:  rexlimddv  2437  mulgt0sr  6862  cnegex  7189  receuap  7650  rexanuz  9587  climcaucn  9870
  Copyright terms: Public domain W3C validator