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Theorem ralbiia 2646
Description: Inference adding restricted universal quantifier to both sides of an equivalence. (Contributed by NM, 26-Nov-2000.)
Hypothesis
Ref Expression
ralbiia.1 (x A → (φψ))
Assertion
Ref Expression
ralbiia (x A φx A ψ)

Proof of Theorem ralbiia
StepHypRef Expression
1 ralbiia.1 . . 3 (x A → (φψ))
21pm5.74i 236 . 2 ((x Aφ) ↔ (x Aψ))
32ralbii2 2642 1 (x A φx A ψ)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wcel 1710  wral 2614
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557
This theorem depends on definitions:  df-bi 177  df-ral 2619
This theorem is referenced by:  dffun8  5134  funcnv3  5157  fncnv  5158  fnres  5199  fvreseq  5398  isoini2  5498
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