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Theorem pm5.53 771
Description: Theorem *5.53 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.53 ((((φ ψ) χ) → θ) ↔ (((φθ) (ψθ)) (χθ)))

Proof of Theorem pm5.53
StepHypRef Expression
1 jaob 758 . 2 ((((φ ψ) χ) → θ) ↔ (((φ ψ) → θ) (χθ)))
2 jaob 758 . . 3 (((φ ψ) → θ) ↔ ((φθ) (ψθ)))
32anbi1i 676 . 2 ((((φ ψ) → θ) (χθ)) ↔ (((φθ) (ψθ)) (χθ)))
41, 3bitri 240 1 ((((φ ψ) χ) → θ) ↔ (((φθ) (ψθ)) (χθ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  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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