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Theorem orddi 839
Description: Double distributive law for disjunction. (Contributed by NM, 12-Aug-1994.)
Assertion
Ref Expression
orddi (((φ ψ) (χ θ)) ↔ (((φ χ) (φ θ)) ((ψ χ) (ψ θ))))

Proof of Theorem orddi
StepHypRef Expression
1 ordir 835 . 2 (((φ ψ) (χ θ)) ↔ ((φ (χ θ)) (ψ (χ θ))))
2 ordi 834 . . 3 ((φ (χ θ)) ↔ ((φ χ) (φ θ)))
3 ordi 834 . . 3 ((ψ (χ θ)) ↔ ((ψ χ) (ψ θ)))
42, 3anbi12i 678 . 2 (((φ (χ θ)) (ψ (χ θ))) ↔ (((φ χ) (φ θ)) ((ψ χ) (ψ θ))))
51, 4bitri 240 1 (((φ ψ) (χ θ)) ↔ (((φ χ) (φ θ)) ((ψ χ) (ψ θ))))
Colors of variables: wff setvar class
Syntax hints:  wb 176   wo 357   wa 358
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360
This theorem is referenced by: (None)
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