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Mirrors > Home > MPE Home > Th. List > 2false | Structured version Visualization version GIF version |
Description: Two falsehoods are equivalent. (Contributed by NM, 4-Apr-2005.) (Proof shortened by Wolf Lammen, 19-May-2013.) |
Ref | Expression |
---|---|
2false.1 | ⊢ ¬ 𝜑 |
2false.2 | ⊢ ¬ 𝜓 |
Ref | Expression |
---|---|
2false | ⊢ (𝜑 ↔ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2false.1 | . . 3 ⊢ ¬ 𝜑 | |
2 | 2false.2 | . . 3 ⊢ ¬ 𝜓 | |
3 | 1, 2 | 2th 266 | . 2 ⊢ (¬ 𝜑 ↔ ¬ 𝜓) |
4 | 3 | con4bii 323 | 1 ⊢ (𝜑 ↔ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 208 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 209 |
This theorem is referenced by: bianfi 536 bifal 1553 dfnul2 4281 co02 6099 0er 8312 00lss 19696 00ply1bas 20391 2lgslem4 25968 signswch 31838 pexmidlem8N 37145 dandysum2p2e4 43324 |
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