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Metamath Proof Explorer

Theorem jao

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)

		Ref	Expression
	Assertion	jao	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 → 𝜓 ) → ( ( 𝜑 ∨ 𝜒 ) → 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm3.44	⊢ ( ( ( 𝜑 → 𝜓 ) ∧ ( 𝜒 → 𝜓 ) ) → ( ( 𝜑 ∨ 𝜒 ) → 𝜓 ) )
2	1	ex	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 → 𝜓 ) → ( ( 𝜑 ∨ 𝜒 ) → 𝜓 ) ) )