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

Metamath Proof Explorer

Theorem pm2.25

Description: Theorem *2.25 of WhiteheadRussell p. 104. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion pm2.25 ( 𝜑 ∨ ( ( 𝜑 ∨ 𝜓 ) → 𝜓 ) )

Proof

Step Hyp Ref Expression
1 orel1 ⊢ ( ¬ 𝜑 → ( ( 𝜑 ∨ 𝜓 ) → 𝜓 ) )
2 1 orri ⊢ ( 𝜑 ∨ ( ( 𝜑 ∨ 𝜓 ) → 𝜓 ) )