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Theorem reximdvai 2413
 Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 14-Nov-2002.)
Hypothesis
Ref Expression
reximdvai.1 (φ → (x A → (ψχ)))
Assertion
Ref Expression
reximdvai (φ → (x A ψx A χ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   χ(x)   A(x)

Proof of Theorem reximdvai
StepHypRef Expression
1 nfv 1418 . 2 xφ
2 reximdvai.1 . 2 (φ → (x A → (ψχ)))
31, 2reximdai 2411 1 (φ → (x A ψx A χ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1390  ∃wrex 2301 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 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305  df-rex 2306 This theorem is referenced by:  reximdv  2414  reximdva  2415  reuind  2738
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