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| Mirrors > Home > MPE Home > Th. List > 3ad2antl1 | Structured version Visualization version GIF version | ||
| Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.) |
| Ref | Expression |
|---|---|
| 3ad2antl.1 | ⊢ ((𝜑 ∧ 𝜒) → 𝜃) |
| Ref | Expression |
|---|---|
| 3ad2antl1 | ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜏) ∧ 𝜒) → 𝜃) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3ad2antl.1 | . . 3 ⊢ ((𝜑 ∧ 𝜒) → 𝜃) | |
| 2 | 1 | adantlr 715 | . 2 ⊢ (((𝜑 ∧ 𝜏) ∧ 𝜒) → 𝜃) |
| 3 | 2 | 3adantl2 1168 | 1 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜏) ∧ 𝜒) → 𝜃) |
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