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Theorem ordir 835
Description: Distributive law for disjunction. (Contributed by NM, 12-Aug-1994.)
Assertion
Ref Expression
ordir (((φ ψ) χ) ↔ ((φ χ) (ψ χ)))

Proof of Theorem ordir
StepHypRef Expression
1 ordi 834 . 2 ((χ (φ ψ)) ↔ ((χ φ) (χ ψ)))
2 orcom 376 . 2 (((φ ψ) χ) ↔ (χ (φ ψ)))
3 orcom 376 . . 3 ((φ χ) ↔ (χ φ))
4 orcom 376 . . 3 ((ψ χ) ↔ (χ ψ))
53, 4anbi12i 678 . 2 (((φ χ) (ψ χ)) ↔ ((χ φ) (χ ψ)))
61, 2, 53bitr4i 268 1 (((φ ψ) χ) ↔ ((φ χ) (ψ χ)))
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:  orddi  839  pm5.62  889  dn1  932  cadan  1392  nchoicelem9  6298
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