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Theorem biadan2 437
Description: Add a conjunction to an equivalence. (Contributed by Jeff Madsen, 20-Jun-2011.)
Hypotheses
Ref Expression
biadan2.1 (𝜑𝜓)
biadan2.2 (𝜓 → (𝜑𝜒))
Assertion
Ref Expression
biadan2 (𝜑 ↔ (𝜓𝜒))

Proof of Theorem biadan2
StepHypRef Expression
1 biadan2.1 . . 3 (𝜑𝜓)
21pm4.71ri 378 . 2 (𝜑 ↔ (𝜓𝜑))
3 biadan2.2 . . 3 (𝜓 → (𝜑𝜒))
43pm5.32i 435 . 2 ((𝜓𝜑) ↔ (𝜓𝜒))
52, 4bitri 177 1 (𝜑 ↔ (𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  elab4g  2714  brab2a  4421  brab2ga  4443  elovmpt2  5729  eqop2  5832  elnnnn0  8282  elixx3g  8871  elfzo2  9109
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