Description: Theorem *4.52 of WhiteheadRussell p. 120. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 5-Nov-2012)
Ref | Expression | ||
---|---|---|---|
Assertion | pm4.52 | ⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) ↔ ¬ ( ¬ 𝜑 ∨ 𝜓 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | annim | ⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) ↔ ¬ ( 𝜑 → 𝜓 ) ) | |
2 | imor | ⊢ ( ( 𝜑 → 𝜓 ) ↔ ( ¬ 𝜑 ∨ 𝜓 ) ) | |
3 | 1 2 | xchbinx | ⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) ↔ ¬ ( ¬ 𝜑 ∨ 𝜓 ) ) |