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Theorem biadan2 449
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 387 . 2 (𝜑 ↔ (𝜓𝜑))
3 biadan2.2 . . 3 (𝜓 → (𝜑𝜒))
43pm5.32i 447 . 2 ((𝜓𝜑) ↔ (𝜓𝜒))
52, 4bitri 183 1 (𝜑 ↔ (𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  elab4g  2804  elpwb  3488  ssdifsn  3619  brab2a  4560  brab2ga  4582  elovmpo  5937  eqop2  6042  elnnnn0  8971  elixx3g  9624  elfzo2  9867  1nprm  11691
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