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Theorem 3jaao 1249
 Description: Inference conjoining and disjoining the antecedents of three implications. (Contributed by Jeff Hankins, 15-Aug-2009.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Hypotheses
Ref Expression
3jaao.1 (φ → (ψχ))
3jaao.2 (θ → (τχ))
3jaao.3 (η → (ζχ))
Assertion
Ref Expression
3jaao ((φ θ η) → ((ψ τ ζ) → χ))

Proof of Theorem 3jaao
StepHypRef Expression
1 3jaao.1 . . 3 (φ → (ψχ))
213ad2ant1 976 . 2 ((φ θ η) → (ψχ))
3 3jaao.2 . . 3 (θ → (τχ))
433ad2ant2 977 . 2 ((φ θ η) → (τχ))
5 3jaao.3 . . 3 (η → (ζχ))
653ad2ant3 978 . 2 ((φ θ η) → (ζχ))
72, 4, 63jaod 1246 1 ((φ θ η) → ((ψ τ ζ) → χ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∨ w3o 933   ∧ w3a 934 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-3an 936 This theorem is referenced by: (None)
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