Theorem jao1i 797

Description: Add a disjunct in the antecedent of an implication. (Contributed by Rodolfo Medina, 24-Sep-2010.)

Hypothesis

Ref	Expression
jao1i.1	⊢ (𝜓 → (𝜒 → 𝜑))

Assertion

Ref	Expression
jao1i	⊢ ((𝜑 ∨ 𝜓) → (𝜒 → 𝜑))

Proof of Theorem jao1i

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 ⊢ (𝜑 → (𝜒 → 𝜑))
2		jao1i.1	. 2 ⊢ (𝜓 → (𝜒 → 𝜑))
3	1, 2	jaoi 717	1 ⊢ ((𝜑 ∨ 𝜓) → (𝜒 → 𝜑))

Syntax hints:   → wi 4   ∨ wo 709

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  nn0enne  12067  dvdsprmpweqnn  12505  dvdsprmpweqle  12506  2lgs  15345  2lgsoddprmlem3  15352