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Theorem bi2anan9r 621
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 620 . 2 ((𝜑𝜃) → ((𝜓𝜏) ↔ (𝜒𝜂)))
43ancoms 446 1 ((𝜃𝜑) → ((𝜓𝜏) ↔ (𝜒𝜂)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 382
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 197  df-an 383
This theorem is referenced by:  efrn2lp  5231  ltsosr  10115  seqf1olem2  13041  seqf1o  13042  pcval  15749  uspgr2wlkeq  26770  fneval  32677  prtlem5  34661  rmydioph  38100  wepwsolem  38131  aomclem8  38150  sprsymrelfolem2  42264
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