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Metamath Proof Explorer

Theorem pm2.64

Description: Theorem *2.64 of WhiteheadRussell p. 107. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion pm2.64 ( ( 𝜑 ∨ 𝜓 ) → ( ( 𝜑 ∨ ¬ 𝜓 ) → 𝜑 ) )

Proof

Step Hyp Ref Expression
1 orel2 ⊢ ( ¬ 𝜓 → ( ( 𝜑 ∨ 𝜓 ) → 𝜑 ) )
2 1 jao1i ⊢ ( ( 𝜑 ∨ ¬ 𝜓 ) → ( ( 𝜑 ∨ 𝜓 ) → 𝜑 ) )
3 2 com12 ⊢ ( ( 𝜑 ∨ 𝜓 ) → ( ( 𝜑 ∨ ¬ 𝜓 ) → 𝜑 ) )