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Mirrors > Home > MPE Home > Th. List > Mathboxes > con2bii2 | Structured version Visualization version GIF version |
Description: A contraposition inference. (Contributed by ML, 18-Oct-2020.) |
Ref | Expression |
---|---|
con2bii2.1 | ⊢ (𝜑 ↔ ¬ 𝜓) |
Ref | Expression |
---|---|
con2bii2 | ⊢ (¬ 𝜑 ↔ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | con2bii2.1 | . . 3 ⊢ (𝜑 ↔ ¬ 𝜓) | |
2 | 1 | con2bii 346 | . 2 ⊢ (𝜓 ↔ ¬ 𝜑) |
3 | 2 | bicomi 213 | 1 ⊢ (¬ 𝜑 ↔ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 195 |
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 196 |
This theorem is referenced by: (None) |
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