Description: Theorem *5.62 of WhiteheadRussell p. 125. (Contributed by Roy F. Longton, 21-Jun-2005)
Ref | Expression | ||
---|---|---|---|
Assertion | pm5.62 | ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∨ ¬ 𝜓 ) ↔ ( 𝜑 ∨ ¬ 𝜓 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exmid | ⊢ ( 𝜓 ∨ ¬ 𝜓 ) | |
2 | ordir | ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∨ ¬ 𝜓 ) ↔ ( ( 𝜑 ∨ ¬ 𝜓 ) ∧ ( 𝜓 ∨ ¬ 𝜓 ) ) ) | |
3 | 1 2 | mpbiran2 | ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∨ ¬ 𝜓 ) ↔ ( 𝜑 ∨ ¬ 𝜓 ) ) |