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| Mirrors > Home > MPE Home > Th. List > 3adant1 | Structured version Visualization version GIF version | ||
| Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Jul-1995.) (Proof shortened by Wolf Lammen, 21-Jun-2022.) |
| Ref | Expression |
|---|---|
| 3adant.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
| Ref | Expression |
|---|---|
| 3adant1 | ⊢ ((𝜃 ∧ 𝜑 ∧ 𝜓) → 𝜒) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3adant.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
| 2 | 1 | adantll 714 | . 2 ⊢ (((𝜃 ∧ 𝜑) ∧ 𝜓) → 𝜒) |
| 3 | 2 | 3impa 1110 | 1 ⊢ ((𝜃 ∧ 𝜑 ∧ 𝜓) → 𝜒) |
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