Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > notbii | Structured version Visualization version GIF version |
Description: Negate both sides of a logical equivalence. (Contributed by NM, 3-Jan-1993.) (Proof shortened by Wolf Lammen, 19-May-2013.) |
Ref | Expression |
---|---|
notbii.1 | ⊢ (𝜑 ↔ 𝜓) |
Ref | Expression |
---|---|
notbii | ⊢ (¬ 𝜑 ↔ ¬ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notbii.1 | . 2 ⊢ (𝜑 ↔ 𝜓) | |
2 | notbi 322 | . 2 ⊢ ((𝜑 ↔ 𝜓) ↔ (¬ 𝜑 ↔ ¬ 𝜓)) | |
3 | 1, 2 | mpbi 233 | 1 ⊢ (¬ 𝜑 ↔ ¬ 𝜓) |
Copyright terms: Public domain | W3C validator |