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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 267 | . 2 ⊢ (¬ 𝜑 ↔ ¬ 𝜓) |
4 | 3 | con4bii 324 | 1 ⊢ (𝜑 ↔ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 209 |
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 210 |
This theorem is referenced by: bianfi 537 bifal 1559 dfnul3 4238 dfnul2OLD 4239 co02 6121 0er 8425 00lss 19975 00ply1bas 21158 2lgslem4 26284 signswch 32249 pexmidlem8N 37726 dandysum2p2e4 44163 |
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