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Theorem andir 838
 Description: Distributive law for conjunction. (Contributed by NM, 12-Aug-1994.)
Assertion
Ref Expression
andir (((φ ψ) χ) ↔ ((φ χ) (ψ χ)))

Proof of Theorem andir
StepHypRef Expression
1 andi 837 . 2 ((χ (φ ψ)) ↔ ((χ φ) (χ ψ)))
2 ancom 437 . 2 (((φ ψ) χ) ↔ (χ (φ ψ)))
3 ancom 437 . . 3 ((φ χ) ↔ (χ φ))
4 ancom 437 . . 3 ((ψ χ) ↔ (χ ψ))
53, 4orbi12i 507 . 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-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 This theorem is referenced by:  anddi  840  cador  1391  rexun  3443  rabun2  3534  reuun2  3538  elimif  3691  xpundir  4833  coundi  5082  nchoicelem18  6306
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