Theorem pm3.48

Description: Theorem *3.48 of WhiteheadRussell p. 114. (Contributed by NM, 28-Jan-1997)

	Ref	Expression
Assertion	pm3.48	⊢ ( ( ( 𝜑 → 𝜓 ) ∧ ( 𝜒 → 𝜃 ) ) → ( ( 𝜑 ∨ 𝜒 ) → ( 𝜓 ∨ 𝜃 ) ) )

Proof

Step	Hyp	Ref	Expression
1		orc	⊢ ( 𝜓 → ( 𝜓 ∨ 𝜃 ) )
2	1	imim2i	⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → ( 𝜓 ∨ 𝜃 ) ) )
3		olc	⊢ ( 𝜃 → ( 𝜓 ∨ 𝜃 ) )
4	3	imim2i	⊢ ( ( 𝜒 → 𝜃 ) → ( 𝜒 → ( 𝜓 ∨ 𝜃 ) ) )
5	2 4	jaao	⊢ ( ( ( 𝜑 → 𝜓 ) ∧ ( 𝜒 → 𝜃 ) ) → ( ( 𝜑 ∨ 𝜒 ) → ( 𝜓 ∨ 𝜃 ) ) )