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Theorem bi2bian9 540
Description: Deduction joining two biconditionals with different antecedents. (Contributed by NM, 12-May-2004.)
Hypotheses
Ref Expression
bi2an9.1 (φ → (ψχ))
bi2an9.2 (θ → (τη))
Assertion
Ref Expression
bi2bian9 ((φ θ) → ((ψτ) ↔ (χη)))

Proof of Theorem bi2bian9
StepHypRef Expression
1 bi2an9.1 . . 3 (φ → (ψχ))
21adantr 261 . 2 ((φ θ) → (ψχ))
3 bi2an9.2 . . 3 (θ → (τη))
43adantl 262 . 2 ((φ θ) → (τη))
52, 4bibi12d 224 1 ((φ θ) → ((ψτ) ↔ (χη)))
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: (None)
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