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Theorem 3orbi123i 1078
Description: Join 3 biconditionals with disjunction. (Contributed by NM, 17-May-1994.)
Hypotheses
Ref Expression
bi3.1 (φψ)
bi3.2 (χθ)
bi3.3 (τη)
Assertion
Ref Expression
3orbi123i ((φ χ τ) ↔ (ψ θ η))

Proof of Theorem 3orbi123i
StepHypRef Expression
1 bi3.1 . . . 4 (φψ)
2 bi3.2 . . . 4 (χθ)
31, 2orbi12i 668 . . 3 ((φ χ) ↔ (ψ θ))
4 bi3.3 . . 3 (τη)
53, 4orbi12i 668 . 2 (((φ χ) τ) ↔ ((ψ θ) η))
6 df-3or 872 . 2 ((φ χ τ) ↔ ((φ χ) τ))
7 df-3or 872 . 2 ((ψ θ η) ↔ ((ψ θ) η))
85, 6, 73bitr4i 201 1 ((φ χ τ) ↔ (ψ θ η))
Colors of variables: wff set class
Syntax hints:  wb 98   wo 616   w3o 870
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617
This theorem depends on definitions:  df-bi 110  df-3or 872
This theorem is referenced by: (None)
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