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Theorem reximdv2 2723
 Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 17-Sep-2003.)
Hypothesis
Ref Expression
reximdv2.1 (φ → ((x A ψ) → (x B χ)))
Assertion
Ref Expression
reximdv2 (φ → (x A ψx B χ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   χ(x)   A(x)   B(x)

Proof of Theorem reximdv2
StepHypRef Expression
1 reximdv2.1 . . 3 (φ → ((x A ψ) → (x B χ)))
21eximdv 1622 . 2 (φ → (x(x A ψ) → x(x B χ)))
3 df-rex 2620 . 2 (x A ψx(x A ψ))
4 df-rex 2620 . 2 (x B χx(x B χ))
52, 3, 43imtr4g 261 1 (φ → (x A ψx B χ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358  ∃wex 1541   ∈ wcel 1710  ∃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 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-rex 2620 This theorem is referenced by:  ssrexv  3331
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