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Theorem biadan2 429
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 ↔ (ψ χ))

Proof of Theorem biadan2
StepHypRef Expression
1 biadan2.1 . . 3 (φψ)
21pm4.71ri 372 . 2 (φ ↔ (ψ φ))
3 biadan2.2 . . 3 (ψ → (φχ))
43pm5.32i 427 . 2 ((ψ φ) ↔ (ψ χ))
52, 4bitri 173 1 (φ ↔ (ψ χ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  elab4g  2685  brab2a  4336  brab2ga  4358  elovmpt2  5643  eqop2  5746  elnnnn0  8001  elixx3g  8540  elfzo2  8777
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