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Mirrors > Home > ILE Home > Th. List > 3adant1 | GIF version |
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Jul-1995.) |
Ref | Expression |
---|---|
3adant.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Ref | Expression |
---|---|
3adant1 | ⊢ ((𝜃 ∧ 𝜑 ∧ 𝜓) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3simpc 903 | . 2 ⊢ ((𝜃 ∧ 𝜑 ∧ 𝜓) → (𝜑 ∧ 𝜓)) | |
2 | 3adant.1 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
3 | 1, 2 | syl 14 | 1 ⊢ ((𝜃 ∧ 𝜑 ∧ 𝜓) → 𝜒) |
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