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Theorem pm5.7 900
Description: Disjunction distributes over the biconditional. Theorem *5.7 of [WhiteheadRussell] p. 125. This theorem is similar to orbidi 898. (Contributed by Roy F. Longton, 21-Jun-2005.)
Assertion
Ref Expression
pm5.7 (((φ χ) ↔ (ψ χ)) ↔ (χ (φψ)))

Proof of Theorem pm5.7
StepHypRef Expression
1 orbidi 898 . 2 ((χ (φψ)) ↔ ((χ φ) ↔ (χ ψ)))
2 orcom 376 . . 3 ((χ φ) ↔ (φ χ))
3 orcom 376 . . 3 ((χ ψ) ↔ (ψ χ))
42, 3bibi12i 306 . 2 (((χ φ) ↔ (χ ψ)) ↔ ((φ χ) ↔ (ψ χ)))
51, 4bitr2i 241 1 (((φ χ) ↔ (ψ χ)) ↔ (χ (φψ)))
Colors of variables: wff setvar class
Syntax hints:  wb 176   wo 357
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
This theorem is referenced by: (None)
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