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

Theorem rexlimdvaa 2527
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 372 . 2  |-  ( (
ph  /\  x  e.  A )  ->  ( ps  ->  ch ) )
32rexlimdva 2526 1  |-  ( ph  ->  ( E. x  e.  A  ps  ->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    e. wcel 1465   E.wrex 2394
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 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-17 1491  ax-ial 1499  ax-i5r 1500
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-ral 2398  df-rex 2399
This theorem is referenced by:  rexlimddv  2531  nnsucuniel  6359  omp1eomlem  6947  ctmlemr  6961  mulgt0sr  7554  axpre-suploclemres  7677  cnegex  7908  receuap  8398  rexanuz  10728  climcaucn  11088  fsumiun  11214  dvdsval2  11423  prmind2  11728  tgcl  12160  neiint  12241  restopnb  12277  iscnp4  12314  blssexps  12525  blssex  12526
  Copyright terms: Public domain W3C validator