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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 215 | . 2 ⊢ (𝜑 → 𝜓) |
4 | 1, 3 | ax-mp 5 | 1 ⊢ 𝜓 |
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