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

Theorem rexlimdvaa 2595
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 ((𝜑 ∧ (𝑥𝐴𝜓)) → 𝜒)
Assertion
Ref Expression
rexlimdvaa (𝜑 → (∃𝑥𝐴 𝜓𝜒))
Distinct variable groups:   𝜑,𝑥   𝜒,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝐴(𝑥)

Proof of Theorem rexlimdvaa
StepHypRef Expression
1 rexlimdvaa.1 . . 3 ((𝜑 ∧ (𝑥𝐴𝜓)) → 𝜒)
21expr 375 . 2 ((𝜑𝑥𝐴) → (𝜓𝜒))
32rexlimdva 2594 1 (𝜑 → (∃𝑥𝐴 𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  wcel 2148  wrex 2456
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-i5r 1535
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-ral 2460  df-rex 2461
This theorem is referenced by:  rexlimddv  2599  nnsucuniel  6499  omp1eomlem  7096  ctmlemr  7110  mulgt0sr  7780  axpre-suploclemres  7903  cnegex  8138  receuap  8629  recapb  8631  rexanuz  11000  climcaucn  11362  fsumiun  11488  dvdsval2  11800  prmind2  12123  pcprmpw2  12335  pockthg  12358  dvdsrvald  13273  dvdsrd  13274  dvdsrex  13278  unitgrp  13296  tgcl  13725  neiint  13806  restopnb  13842  iscnp4  13879  blssexps  14090  blssex  14091  lgsne0  14600
  Copyright terms: Public domain W3C validator