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Theorem bi2anan9r 639
Description: Deduction joining two equivalences to form equivalence of conjunctions. (Contributed by NM, 19-Feb-1996.)
Hypotheses
Ref Expression
bi2an9.1 (𝜑 → (𝜓𝜒))
bi2an9.2 (𝜃 → (𝜏𝜂))
Assertion
Ref Expression
bi2anan9r ((𝜃𝜑) → ((𝜓𝜏) ↔ (𝜒𝜂)))

Proof of Theorem bi2anan9r
StepHypRef Expression
1 bi2an9.1 . . 3 (𝜑 → (𝜓𝜒))
2 bi2an9.2 . . 3 (𝜃 → (𝜏𝜂))
31, 2bi2anan9 638 . 2 ((𝜑𝜃) → ((𝜓𝜏) ↔ (𝜒𝜂)))
43ancoms 458 1 ((𝜃𝜑) → ((𝜓𝜏) ↔ (𝜒𝜂)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 206  wa 395
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 207  df-an 396
This theorem is referenced by:  efrn2lp  5666  ltsosr  11134  seqf1olem2  14083  seqf1o  14084  pcval  16882  sltlpss  27945  uspgr2wlkeq  29664  satf0op  35382  fmlafvel  35390  fneval  36353  prtlem5  38861  prjspval  42613  rmydioph  43026  wepwsolem  43054  aomclem8  43073  sprsymrelfolem2  47480
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