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Theorem rexlimdvaa 2412
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 (x A ψ)) → χ)
Assertion
Ref Expression
rexlimdvaa (φ → (x A 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 (x A ψ)) → χ)
21expr 357 . 2 ((φ x A) → (ψχ))
32rexlimdva 2411 1 (φ → (x A 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:  rexlimddv  2415  mulgt0sr  6522  cnegex  6776
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