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Mirrors > Home > MPE Home > Th. List > mpbir | Structured version Visualization version GIF version |
Description: An inference from a biconditional, related to modus ponens. (Contributed by NM, 28-Dec-1992.) |
Ref | Expression |
---|---|
mpbir.min | ⊢ 𝜓 |
mpbir.maj | ⊢ (𝜑 ↔ 𝜓) |
Ref | Expression |
---|---|
mpbir | ⊢ 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpbir.min | . 2 ⊢ 𝜓 | |
2 | mpbir.maj | . . 3 ⊢ (𝜑 ↔ 𝜓) | |
3 | 2 | biimpri 231 | . 2 ⊢ (𝜓 → 𝜑) |
4 | 1, 3 | ax-mp 5 | 1 ⊢ 𝜑 |
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