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Theorem ralimdv2 2383
Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 1-Feb-2005.)
Hypothesis
Ref Expression
ralimdv2.1 (φ → ((x Aψ) → (x Bχ)))
Assertion
Ref Expression
ralimdv2 (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 ralimdv2
StepHypRef Expression
1 ralimdv2.1 . . 3 (φ → ((x Aψ) → (x Bχ)))
21alimdv 1756 . 2 (φ → (x(x Aψ) → x(x Bχ)))
3 df-ral 2305 . 2 (x A ψx(x Aψ))
4 df-ral 2305 . 2 (x B χx(x Bχ))
52, 3, 43imtr4g 194 1 (φ → (x A ψx B χ))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1240   wcel 1390  wral 2300
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-17 1416
This theorem depends on definitions:  df-bi 110  df-ral 2305
This theorem is referenced by:  ssralv  2998
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