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Mirrors > Home > MPE Home > Th. List > con4bii | Structured version Visualization version GIF version |
Description: A contraposition inference. (Contributed by NM, 21-May-1994.) |
Ref | Expression |
---|---|
con4bii.1 | ⊢ (¬ 𝜑 ↔ ¬ 𝜓) |
Ref | Expression |
---|---|
con4bii | ⊢ (𝜑 ↔ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | con4bii.1 | . 2 ⊢ (¬ 𝜑 ↔ ¬ 𝜓) | |
2 | notbi 322 | . 2 ⊢ ((𝜑 ↔ 𝜓) ↔ (¬ 𝜑 ↔ ¬ 𝜓)) | |
3 | 1, 2 | mpbir 234 | 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: 2false 379 equsexvw 2011 cbvex 2406 cbvexvOLD 2410 cbvex2 2423 2ralor 3322 gencbval 3499 snnzb 4614 raldifsnb 4689 uni0b 4826 opab0 5406 ceqsralv2 33069 tsna1 35582 |
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