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Theorem rexlimdvv 2417
Description: Inference from Theorem 19.23 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 22-Jul-2004.)
Hypothesis
Ref Expression
rexlimdvv.1 (φ → ((x A y B) → (ψχ)))
Assertion
Ref Expression
rexlimdvv (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 rexlimdvv
StepHypRef Expression
1 rexlimdvv.1 . . . 4 (φ → ((x A y B) → (ψχ)))
21expdimp 246 . . 3 ((φ x A) → (y B → (ψχ)))
32rexlimdv 2410 . 2 ((φ x A) → (y B ψχ))
43rexlimdva 2411 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:  rexlimdvva  2418  f1oiso2  5391  genpcdl  6374  genpcuu  6375  distrlem1prl  6421  distrlem1pru  6422  distrlem5prl  6425  distrlem5pru  6426  recexprlemss1l  6469  recexprlemss1u  6470
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