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

Theorem rexlimdvaa 2575
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 373 . 2  |-  ( (
ph  /\  x  e.  A )  ->  ( ps  ->  ch ) )
32rexlimdva 2574 1  |-  ( ph  ->  ( E. x  e.  A  ps  ->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    e. wcel 2128   E.wrex 2436
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-4 1490  ax-17 1506  ax-ial 1514  ax-i5r 1515
This theorem depends on definitions:  df-bi 116  df-nf 1441  df-ral 2440  df-rex 2441
This theorem is referenced by:  rexlimddv  2579  nnsucuniel  6442  omp1eomlem  7038  ctmlemr  7052  mulgt0sr  7698  axpre-suploclemres  7821  cnegex  8053  receuap  8543  rexanuz  10888  climcaucn  11248  fsumiun  11374  dvdsval2  11686  prmind2  11997  tgcl  12475  neiint  12556  restopnb  12592  iscnp4  12629  blssexps  12840  blssex  12841
  Copyright terms: Public domain W3C validator