This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem pm2.36

Description: Theorem *2.36 of WhiteheadRussell p. 105. (Contributed by NM, 6-Mar-2008)

Ref Expression
Assertion pm2.36 ( ( 𝜓 → 𝜒 ) → ( ( 𝜑 ∨ 𝜓 ) → ( 𝜒 ∨ 𝜑 ) ) )

Proof

Step Hyp Ref Expression
1 pm1.4 ⊢ ( ( 𝜑 ∨ 𝜓 ) → ( 𝜓 ∨ 𝜑 ) )
2 pm2.38 ⊢ ( ( 𝜓 → 𝜒 ) → ( ( 𝜓 ∨ 𝜑 ) → ( 𝜒 ∨ 𝜑 ) ) )
3 1 2 syl5 ⊢ ( ( 𝜓 → 𝜒 ) → ( ( 𝜑 ∨ 𝜓 ) → ( 𝜒 ∨ 𝜑 ) ) )