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| Mirrors > Home > MPE Home > Th. List > mpcom | Structured version Visualization version GIF version | ||
| Description: Modus ponens inference with commutation of antecedents. Commuted form of mpd 15. (Contributed by NM, 17-Mar-1996.) |
| Ref | Expression |
|---|---|
| mpcom.1 | ⊢ (𝜓 → 𝜑) |
| mpcom.2 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
| Ref | Expression |
|---|---|
| mpcom | ⊢ (𝜓 → 𝜒) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mpcom.1 | . 2 ⊢ (𝜓 → 𝜑) | |
| 2 | mpcom.2 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
| 3 | 2 | com12 32 | . 2 ⊢ (𝜓 → (𝜑 → 𝜒)) |
| 4 | 1, 3 | mpd 15 | 1 ⊢ (𝜓 → 𝜒) |
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