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Mirrors > Home > MPE Home > Th. List > ad2ant2r | Structured version Visualization version GIF version |
Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 8-Jan-2006.) |
Ref | Expression |
---|---|
ad2ant2.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Ref | Expression |
---|---|
ad2ant2r | ⊢ (((𝜑 ∧ 𝜃) ∧ (𝜓 ∧ 𝜏)) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad2ant2.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
2 | 1 | adantrr 717 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜏)) → 𝜒) |
3 | 2 | adantlr 715 | 1 ⊢ (((𝜑 ∧ 𝜃) ∧ (𝜓 ∧ 𝜏)) → 𝜒) |
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