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Theorem jaob 758
 Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. (Contributed by NM, 30-May-1994.) (Proof shortened by Wolf Lammen, 9-Dec-2012.)
Assertion
Ref Expression
jaob (((φ χ) → ψ) ↔ ((φψ) (χψ)))

Proof of Theorem jaob
StepHypRef Expression
1 pm2.67-2 391 . . 3 (((φ χ) → ψ) → (φψ))
2 olc 373 . . . 4 (χ → (φ χ))
32imim1i 54 . . 3 (((φ χ) → ψ) → (χψ))
41, 3jca 518 . 2 (((φ χ) → ψ) → ((φψ) (χψ)))
5 pm3.44 497 . 2 (((φψ) (χψ)) → ((φ χ) → ψ))
64, 5impbii 180 1 (((φ χ) → ψ) ↔ ((φψ) (χψ)))
 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:  pm4.77  762  pm5.53  771  pm4.83  895  unss  3437  ralunb  3444  intun  3958  intpr  3959
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