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Theorem jao 498
Description: Disjunction of antecedents. Compare Theorem *3.44 of [WhiteheadRussell] p. 113. (Contributed by NM, 5-Apr-1994.) (Proof shortened by Wolf Lammen, 4-Apr-2013.)
Assertion
Ref Expression
jao ((φψ) → ((χψ) → ((φ χ) → ψ)))

Proof of Theorem jao
StepHypRef Expression
1 pm3.44 497 . 2 (((φψ) (χψ)) → ((φ χ) → ψ))
21ex 423 1 ((φψ) → ((χψ) → ((φ χ) → ψ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4   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  df-an 360
This theorem is referenced by:  3jao  1243
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