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Theorem ral2imi 2379
Description: Inference quantifying antecedent, nested antecedent, and consequent, with a strong hypothesis. (Contributed by NM, 19-Dec-2006.)
Hypothesis
Ref Expression
ral2imi.1 (φ → (ψχ))
Assertion
Ref Expression
ral2imi (x A φ → (x A ψx A χ))

Proof of Theorem ral2imi
StepHypRef Expression
1 ral2imi.1 . . 3 (φ → (ψχ))
21ralimi 2378 . 2 (x A φx A (ψχ))
3 ralim 2374 . 2 (x A (ψχ) → (x A ψx A χ))
42, 3syl 14 1 (x A φ → (x A ψx A χ))
Colors of variables: wff set class
Syntax hints:  wi 4  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
This theorem depends on definitions:  df-bi 110  df-ral 2305
This theorem is referenced by:  r19.26  2435  iinerm  6114  bj-findis  9439
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