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Theorem ordir 718
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 717 . 2 ((χ (φ ψ)) ↔ ((χ φ) (χ ψ)))
2 orcom 634 . 2 (((φ ψ) χ) ↔ (χ (φ ψ)))
3 orcom 634 . . 3 ((φ χ) ↔ (χ φ))
4 orcom 634 . . 3 ((ψ χ) ↔ (χ ψ))
53, 4anbi12i 436 . 2 (((φ χ) (ψ χ)) ↔ ((χ φ) (χ ψ)))
61, 2, 53bitr4i 201 1 (((φ ψ) χ) ↔ ((φ χ) (ψ χ)))
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98   wo 616
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
This theorem is referenced by:  orddi  721  pm5.62dc  840  dn1dc  855  suc11g  4219  bj-peano4  7324
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