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Metamath Proof Explorer
Description: Two propositions are equivalent if they are both false. Theorem *5.21 of
WhiteheadRussell p. 124. (Contributed by NM, 21-May-1994)
|
|
Ref |
Expression |
|
Assertion |
pm5.21 |
⊢ ( ( ¬ 𝜑 ∧ ¬ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
pm5.21im |
⊢ ( ¬ 𝜑 → ( ¬ 𝜓 → ( 𝜑 ↔ 𝜓 ) ) ) |
| 2 |
1
|
imp |
⊢ ( ( ¬ 𝜑 ∧ ¬ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) ) |