Metamath Proof Explorer

Theorem pm5.15

Description: Theorem *5.15 of WhiteheadRussell p. 124. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 15-Oct-2013)

Ref Expression
Assertion pm5.15 ( ( 𝜑 ↔ 𝜓 ) ∨ ( 𝜑 ↔ ¬ 𝜓 ) )

Proof

Step Hyp Ref Expression
1 xor3 ⊢ ( ¬ ( 𝜑 ↔ 𝜓 ) ↔ ( 𝜑 ↔ ¬ 𝜓 ) )
2 1 biimpi ⊢ ( ¬ ( 𝜑 ↔ 𝜓 ) → ( 𝜑 ↔ ¬ 𝜓 ) )
3 2 orri ⊢ ( ( 𝜑 ↔ 𝜓 ) ∨ ( 𝜑 ↔ ¬ 𝜓 ) )