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Theorem ralimdv 2382
 Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 8-Oct-2003.)
Hypothesis
Ref Expression
ralimdv.1 (φ → (ψχ))
Assertion
Ref Expression
ralimdv (φ → (x A ψx A χ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   χ(x)   A(x)

Proof of Theorem ralimdv
StepHypRef Expression
1 ralimdv.1 . . 3 (φ → (ψχ))
21adantr 261 . 2 ((φ x A) → (ψχ))
32ralimdva 2381 1 (φ → (x A ψx A χ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ 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-4 1397  ax-17 1416 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305 This theorem is referenced by:  poss  4026  sess1  4059  sess2  4060  riinint  4536  dffo4  5258  dffo5  5259  isoini2  5401  rdgivallem  5908  iinerm  6114
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