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

Theorem rexlimdvva 2418
Description: Inference from Theorem 19.23 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 18-Jun-2014.)
Hypothesis
Ref Expression
rexlimdvva.1 ((φ (x A y B)) → (ψχ))
Assertion
Ref Expression
rexlimdvva (φ → (x A y B ψχ))
Distinct variable groups:   x,y,φ   χ,x,y   y,A
Allowed substitution hints:   ψ(x,y)   A(x)   B(x,y)

Proof of Theorem rexlimdvva
StepHypRef Expression
1 rexlimdvva.1 . . 3 ((φ (x A y B)) → (ψχ))
21ex 108 . 2 (φ → ((x A y B) → (ψχ)))
32rexlimdvv 2417 1 (φ → (x A y B ψχ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   wcel 1374  wrex 2285
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1316  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-4 1381  ax-17 1400  ax-ial 1409  ax-i5r 1410
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-ral 2289  df-rex 2290
This theorem is referenced by:  ovelrn  5572  f1o2ndf1  5772  eroveu  6108  eroprf  6110  genipv  6363  genpelvl  6366  genpelvu  6367  genprndl  6376  genprndu  6377  addlocpr  6391  ltsopr  6433  ltaddpr  6434  ltexprlemfl  6446  ltexprlemrl  6447  ltexprlemfu  6448  ltexprlemru  6449  addcanprleml  6451
  Copyright terms: Public domain W3C validator