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Theorem jao1i 842
Description: Add a disjunct in the antecedent of an implication. (Contributed by Rodolfo Medina, 24-Sep-2010.)
Hypothesis
Ref Expression
jao1i.1 (𝜓 → (𝜒𝜑))
Assertion
Ref Expression
jao1i ((𝜑𝜓) → (𝜒𝜑))

Proof of Theorem jao1i
StepHypRef Expression
1 ax-1 6 . 2 (𝜑 → (𝜒𝜑))
2 jao1i.1 . 2 (𝜓 → (𝜒𝜑))
31, 2jaoi 393 1 ((𝜑𝜓) → (𝜒𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 382
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 197  df-or 384
This theorem is referenced by:  pm2.64  847  pm2.82  915  nn0enne  15141  dvdsprmpweqnn  15636  dvdsprmpweqle  15637  2lgsoddprmlem3  25184  prtlem14  34478
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