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Mirrors > Home > MPE Home > Th. List > ad2antll | Structured version Visualization version GIF version |
Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 19-Oct-1999.) |
Ref | Expression |
---|---|
ad2ant.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
ad2antll | ⊢ ((𝜒 ∧ (𝜃 ∧ 𝜑)) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad2ant.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | 1 | adantl 485 | . 2 ⊢ ((𝜃 ∧ 𝜑) → 𝜓) |
3 | 2 | adantl 485 | 1 ⊢ ((𝜒 ∧ (𝜃 ∧ 𝜑)) → 𝜓) |
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