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| Mirrors > Home > MPE Home > Th. List > mpbi | Structured version Visualization version GIF version | ||
| Description: An inference from a biconditional, related to modus ponens. (Contributed by NM, 11-May-1993.) |
| Ref | Expression |
|---|---|
| mpbi.min | ⊢ 𝜑 |
| mpbi.maj | ⊢ (𝜑 ↔ 𝜓) |
| Ref | Expression |
|---|---|
| mpbi | ⊢ 𝜓 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mpbi.min | . 2 ⊢ 𝜑 | |
| 2 | mpbi.maj | . . 3 ⊢ (𝜑 ↔ 𝜓) | |
| 3 | 2 | biimpi 216 | . 2 ⊢ (𝜑 → 𝜓) |
| 4 | 1, 3 | ax-mp 5 | 1 ⊢ 𝜓 |
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