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| Mirrors > Home > MPE Home > Th. List > ad3antlr | Structured version Visualization version GIF version | ||
| Description: Deduction adding three conjuncts to antecedent. (Contributed by Mario Carneiro, 5-Jan-2017.) (Proof shortened by Wolf Lammen, 5-Apr-2022.) |
| Ref | Expression |
|---|---|
| ad2ant.1 | ⊢ (𝜑 → 𝜓) |
| Ref | Expression |
|---|---|
| ad3antlr | ⊢ ((((𝜒 ∧ 𝜑) ∧ 𝜃) ∧ 𝜏) → 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ad2ant.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
| 2 | 1 | adantl 481 | . 2 ⊢ ((𝜒 ∧ 𝜑) → 𝜓) |
| 3 | 2 | ad2antrr 726 | 1 ⊢ ((((𝜒 ∧ 𝜑) ∧ 𝜃) ∧ 𝜏) → 𝜓) |
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