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Mirrors > Home > MPE Home > Th. List > adantlrr | Structured version Visualization version GIF version |
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.) |
Ref | Expression |
---|---|
adantl2.1 | ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
adantlrr | ⊢ (((𝜑 ∧ (𝜓 ∧ 𝜏)) ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 475 | . 2 ⊢ ((𝜓 ∧ 𝜏) → 𝜓) | |
2 | adantl2.1 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) | |
3 | 1, 2 | sylanl2 668 | 1 ⊢ (((𝜑 ∧ (𝜓 ∧ 𝜏)) ∧ 𝜒) → 𝜃) |
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