This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Express a conjunction in terms of a negated implication. (Contributed by NM, 2-Aug-1994)
|
|
Ref |
Expression |
|
Assertion |
annim |
⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) ↔ ¬ ( 𝜑 → 𝜓 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
iman |
⊢ ( ( 𝜑 → 𝜓 ) ↔ ¬ ( 𝜑 ∧ ¬ 𝜓 ) ) |
| 2 |
1
|
con2bii |
⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) ↔ ¬ ( 𝜑 → 𝜓 ) ) |