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Theorem reximdai 2722
 Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 31-Aug-1999.)
Hypotheses
Ref Expression
reximdai.1 xφ
reximdai.2 (φ → (x A → (ψχ)))
Assertion
Ref Expression
reximdai (φ → (x A ψx A χ))

Proof of Theorem reximdai
StepHypRef Expression
1 reximdai.1 . . 3 xφ
2 reximdai.2 . . 3 (φ → (x A → (ψχ)))
31, 2ralrimi 2695 . 2 (φx A (ψχ))
4 rexim 2718 . 2 (x A (ψχ) → (x A ψx A χ))
53, 4syl 15 1 (φ → (x A ψx A χ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  Ⅎwnf 1544   ∈ wcel 1710  ∀wral 2614  ∃wrex 2615 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-ral 2619  df-rex 2620 This theorem is referenced by:  reximdvai  2724  chfnrn  5399
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