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

Theorem rexlimdvw 2492
Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 18-Jun-2014.)
Hypothesis
Ref Expression
rexlimdvw.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
rexlimdvw  |-  ( ph  ->  ( E. x  e.  A  ps  ->  ch ) )
Distinct variable groups:    ph, x    ch, x
Allowed substitution hints:    ps( x)    A( x)

Proof of Theorem rexlimdvw
StepHypRef Expression
1 rexlimdvw.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21a1d 22 . 2  |-  ( ph  ->  ( x  e.  A  ->  ( ps  ->  ch ) ) )
32rexlimdv 2488 1  |-  ( ph  ->  ( E. x  e.  A  ps  ->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1438   E.wrex 2360
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-17 1464  ax-ial 1472  ax-i5r 1473
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-ral 2364  df-rex 2365
This theorem is referenced by:  qsss  6351  fodjuomnilemdc  6799  ltpopr  7154  ltsopr  7155  ltexprlemlol  7161  ltexprlemupu  7163  cauappcvgprlemrnd  7209  caucvgprlemrnd  7232  caucvgprprlemrnd  7260  climuni  10681  bj-findis  11874  nnpredcl  11890
  Copyright terms: Public domain W3C validator