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Metamath Proof Explorer

Theorem jaoi

Description: Inference disjoining the antecedents of two implications. (Contributed by NM, 5-Apr-1994)

Ref Expression
Hypotheses jaoi.1 ⊢ ( 𝜑 → 𝜓 )
jaoi.2 ⊢ ( 𝜒 → 𝜓 )
Assertion jaoi ( ( 𝜑 ∨ 𝜒 ) → 𝜓 )

Proof

Step Hyp Ref Expression
1 jaoi.1 ⊢ ( 𝜑 → 𝜓 )
2 jaoi.2 ⊢ ( 𝜒 → 𝜓 )
3 pm2.53 ⊢ ( ( 𝜑 ∨ 𝜒 ) → ( ¬ 𝜑 → 𝜒 ) )
4 3 2 syl6 ⊢ ( ( 𝜑 ∨ 𝜒 ) → ( ¬ 𝜑 → 𝜓 ) )
5 4 1 pm2.61d2 ⊢ ( ( 𝜑 ∨ 𝜒 ) → 𝜓 )