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Theorem reximdv2 2412
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 1757 . 2 (φ → (x(x A ψ) → x(x B χ)))
3 df-rex 2306 . 2 (x A ψx(x A ψ))
4 df-rex 2306 . 2 (x B χx(x B χ))
52, 3, 43imtr4g 194 1 (φ → (x A ψx B χ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wex 1378   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-rex 2306
This theorem is referenced by:  ssrexv  2999  ssimaex  5177
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