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Metamath Proof Explorer

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 ) ) )