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Mirrors > Home > MPE Home > Th. List > con1b | Structured version Visualization version GIF version |
Description: Contraposition. Bidirectional version of con1 148. (Contributed by NM, 3-Jan-1993.) |
Ref | Expression |
---|---|
con1b | ⊢ ((¬ 𝜑 → 𝜓) ↔ (¬ 𝜓 → 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | con1 148 | . 2 ⊢ ((¬ 𝜑 → 𝜓) → (¬ 𝜓 → 𝜑)) | |
2 | con1 148 | . 2 ⊢ ((¬ 𝜓 → 𝜑) → (¬ 𝜑 → 𝜓)) | |
3 | 1, 2 | impbii 212 | 1 ⊢ ((¬ 𝜑 → 𝜓) ↔ (¬ 𝜓 → 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ 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: eximal 1790 r19.23v 3198 pwssun 5451 ist1-2 22244 cmpfi 22305 dchrelbas2 26118 |
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