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Theorem ralbiia 2332
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 169 . 2 ((x Aφ) ↔ (x Aψ))
32ralbii2 2328 1 (x A φx A ψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   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
This theorem depends on definitions:  df-bi 110  df-ral 2305
This theorem is referenced by:  poinxp  4352  soinxp  4353  seinxp  4354  dffun8  4872  funcnv3  4904  fncnv  4908  fnres  4958  fvreseq  5214  isoini2  5401  smores  5848
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