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Mirrors > Home > ILE Home > Th. List > ad3antrrr | GIF version |
Description: Deduction adding three conjuncts to antecedent. (Contributed by NM, 28-Jul-2012.) |
Ref | Expression |
---|---|
ad2ant.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
ad3antrrr | ⊢ ((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad2ant.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | 1 | adantr 274 | . 2 ⊢ ((𝜑 ∧ 𝜒) → 𝜓) |
3 | 2 | ad2antrr 485 | 1 ⊢ ((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜓) |
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