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

Theorem rexlimdvw 2551
Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 18-Jun-2014.)
Hypothesis
Ref Expression
rexlimdvw.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
rexlimdvw (𝜑 → (∃𝑥𝐴 𝜓𝜒))
Distinct variable groups:   𝜑,𝑥   𝜒,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝐴(𝑥)

Proof of Theorem rexlimdvw
StepHypRef Expression
1 rexlimdvw.1 . . 3 (𝜑 → (𝜓𝜒))
21a1d 22 . 2 (𝜑 → (𝑥𝐴 → (𝜓𝜒)))
32rexlimdv 2546 1 (𝜑 → (∃𝑥𝐴 𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1480  wrex 2415
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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-i5r 1515
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-ral 2419  df-rex 2420
This theorem is referenced by:  nnpredcl  4531  qsss  6481  fodjuomnilemdc  7009  ltpopr  7396  ltsopr  7397  ltexprlemlol  7403  ltexprlemupu  7405  cauappcvgprlemrnd  7451  caucvgprlemrnd  7474  caucvgprprlemrnd  7502  suplocexprlemss  7516  suplocexprlemrl  7518  suplocsrlempr  7608  climuni  11055  cncnp2m  12385  bj-findis  13162
  Copyright terms: Public domain W3C validator