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Mirrors > Home > MPE Home > Th. List > mp3an1 | Structured version Visualization version GIF version |
Description: An inference based on modus ponens. (Contributed by NM, 21-Nov-1994.) |
Ref | Expression |
---|---|
mp3an1.1 | ⊢ 𝜑 |
mp3an1.2 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
mp3an1 | ⊢ ((𝜓 ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mp3an1.1 | . 2 ⊢ 𝜑 | |
2 | mp3an1.2 | . . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
3 | 2 | 3expb 1258 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃) |
4 | 1, 3 | mpan 702 | 1 ⊢ ((𝜓 ∧ 𝜒) → 𝜃) |
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