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Metamath Proof Explorer
Description: Theorem *4.8 of WhiteheadRussell p. 122. (Contributed by NM, 3-Jan-2005)
|
|
Ref |
Expression |
|
Assertion |
pm4.8 |
⊢ ( ( 𝜑 → ¬ 𝜑 ) ↔ ¬ 𝜑 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
pm2.01 |
⊢ ( ( 𝜑 → ¬ 𝜑 ) → ¬ 𝜑 ) |
| 2 |
|
ax-1 |
⊢ ( ¬ 𝜑 → ( 𝜑 → ¬ 𝜑 ) ) |
| 3 |
1 2
|
impbii |
⊢ ( ( 𝜑 → ¬ 𝜑 ) ↔ ¬ 𝜑 ) |