Description: Two falsehoods are equivalent. (Contributed by NM, 4-Apr-2005) (Proof shortened by Wolf Lammen, 19-May-2013)
Ref | Expression | ||
---|---|---|---|
Hypotheses | 2false.1 | ⊢ ¬ 𝜑 | |
2false.2 | ⊢ ¬ 𝜓 | ||
Assertion | 2false | ⊢ ( 𝜑 ↔ 𝜓 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2false.1 | ⊢ ¬ 𝜑 | |
2 | 2false.2 | ⊢ ¬ 𝜓 | |
3 | 1 2 | 2th | ⊢ ( ¬ 𝜑 ↔ ¬ 𝜓 ) |
4 | 3 | con4bii | ⊢ ( 𝜑 ↔ 𝜓 ) |