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Mirrors > Home > MPE Home > Th. List > mpbird | Structured version Visualization version GIF version |
Description: A deduction from a biconditional, related to modus ponens. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
mpbird.min | ⊢ (𝜑 → 𝜒) |
mpbird.maj | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
Ref | Expression |
---|---|
mpbird | ⊢ (𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpbird.min | . 2 ⊢ (𝜑 → 𝜒) | |
2 | mpbird.maj | . . 3 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
3 | 2 | biimprd 251 | . 2 ⊢ (𝜑 → (𝜒 → 𝜓)) |
4 | 1, 3 | mpd 15 | 1 ⊢ (𝜑 → 𝜓) |
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