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| Mirrors > Home > MPE Home > Th. List > 3ad2ant2 | Structured version Visualization version GIF version | ||
| Description: Deduction adding conjuncts to an antecedent. (Contributed by NM, 21-Apr-2005.) |
| Ref | Expression |
|---|---|
| 3ad2ant.1 | ⊢ (𝜑 → 𝜒) |
| Ref | Expression |
|---|---|
| 3ad2ant2 | ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜃) → 𝜒) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3ad2ant.1 | . . 3 ⊢ (𝜑 → 𝜒) | |
| 2 | 1 | adantr 480 | . 2 ⊢ ((𝜑 ∧ 𝜃) → 𝜒) |
| 3 | 2 | 3adant1 1131 | 1 ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜃) → 𝜒) |
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