Metamath Proof Explorer

Theorem orim2

Description: Axiom *1.6 (Sum) of WhiteheadRussell p. 97. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion orim2 ( ( 𝜓 → 𝜒 ) → ( ( 𝜑 ∨ 𝜓 ) → ( 𝜑 ∨ 𝜒 ) ) )

Proof

Step Hyp Ref Expression
1 id ⊢ ( ( 𝜓 → 𝜒 ) → ( 𝜓 → 𝜒 ) )
2 1 orim2d ⊢ ( ( 𝜓 → 𝜒 ) → ( ( 𝜑 ∨ 𝜓 ) → ( 𝜑 ∨ 𝜒 ) ) )