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Mirrors > Home > MPE Home > Th. List > adantrr | Structured version Visualization version GIF version |
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 4-May-1994.) (Proof shortened by Wolf Lammen, 24-Nov-2012.) |
Ref | Expression |
---|---|
adant2.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Ref | Expression |
---|---|
adantrr | ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜃)) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 486 | . 2 ⊢ ((𝜓 ∧ 𝜃) → 𝜓) | |
2 | adant2.1 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
3 | 1, 2 | sylan2 596 | 1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜃)) → 𝜒) |
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