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Metamath Proof Explorer
Description: Theorem *4.54 of WhiteheadRussell p. 120. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 5-Nov-2012)
|
|
Ref |
Expression |
|
Assertion |
pm4.54 |
⊢ ( ( ¬ 𝜑 ∧ 𝜓 ) ↔ ¬ ( 𝜑 ∨ ¬ 𝜓 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
df-an |
⊢ ( ( ¬ 𝜑 ∧ 𝜓 ) ↔ ¬ ( ¬ 𝜑 → ¬ 𝜓 ) ) |
| 2 |
|
pm4.66 |
⊢ ( ( ¬ 𝜑 → ¬ 𝜓 ) ↔ ( 𝜑 ∨ ¬ 𝜓 ) ) |
| 3 |
1 2
|
xchbinx |
⊢ ( ( ¬ 𝜑 ∧ 𝜓 ) ↔ ¬ ( 𝜑 ∨ ¬ 𝜓 ) ) |