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Theorem ralimia 2379
Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 19-Jul-1996.)
Hypothesis
Ref Expression
ralimia.1 (x A → (φψ))
Assertion
Ref Expression
ralimia (x A φx A ψ)

Proof of Theorem ralimia
StepHypRef Expression
1 ralimia.1 . . 3 (x A → (φψ))
21a2i 11 . 2 ((x Aφ) → (x Aψ))
32ralimi2 2378 1 (x A φx A ψ)
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1393  wral 2303
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 1336  ax-gen 1338
This theorem depends on definitions:  df-bi 110  df-ral 2308
This theorem is referenced by:  ralimiaa  2380  ralimi  2381  r19.12  2419  rr19.3v  2679  rr19.28v  2680  ffvresb  5274  f1mpt  5356  peano2nnnn  6819  peano5nnnn  6856  peano5nni  7790  peano2nn  7799
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