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Theorem ralrimd 2391
Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 16-Feb-2004.)
Hypotheses
Ref Expression
ralrimd.1 xφ
ralrimd.2 xψ
ralrimd.3 (φ → (ψ → (x Aχ)))
Assertion
Ref Expression
ralrimd (φ → (ψx A χ))

Proof of Theorem ralrimd
StepHypRef Expression
1 ralrimd.1 . . 3 xφ
2 ralrimd.2 . . 3 xψ
3 ralrimd.3 . . 3 (φ → (ψ → (x Aχ)))
41, 2, 3alrimd 1498 . 2 (φ → (ψx(x Aχ)))
5 df-ral 2305 . 2 (x A χx(x Aχ))
64, 5syl6ibr 151 1 (φ → (ψx A χ))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1240  wnf 1346   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
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305
This theorem is referenced by:  ralrimdv  2392  fliftfun  5379  fzrevral  8717
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