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Mirrors > Home > MPE Home > Th. List > 3adant1r | Structured version Visualization version GIF version |
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.) |
Ref | Expression |
---|---|
3adant1l.1 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
3adant1r | ⊢ (((𝜑 ∧ 𝜏) ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3adant1l.1 | . . . 4 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
2 | 1 | 3expb 1266 | . . 3 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃) |
3 | 2 | adantlr 751 | . 2 ⊢ (((𝜑 ∧ 𝜏) ∧ (𝜓 ∧ 𝜒)) → 𝜃) |
4 | 3 | 3impb 1260 | 1 ⊢ (((𝜑 ∧ 𝜏) ∧ 𝜓 ∧ 𝜒) → 𝜃) |
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