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Mirrors > Home > MPE Home > Th. List > anim12d | Structured version Visualization version GIF version |
Description: Conjoin antecedents and consequents in a deduction. (Contributed by NM, 3-Apr-1994.) (Proof shortened by Wolf Lammen, 18-Dec-2013.) |
Ref | Expression |
---|---|
anim12d.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
anim12d.2 | ⊢ (𝜑 → (𝜃 → 𝜏)) |
Ref | Expression |
---|---|
anim12d | ⊢ (𝜑 → ((𝜓 ∧ 𝜃) → (𝜒 ∧ 𝜏))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anim12d.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | anim12d.2 | . 2 ⊢ (𝜑 → (𝜃 → 𝜏)) | |
3 | idd 24 | . 2 ⊢ (𝜑 → ((𝜒 ∧ 𝜏) → (𝜒 ∧ 𝜏))) | |
4 | 1, 2, 3 | syl2and 611 | 1 ⊢ (𝜑 → ((𝜓 ∧ 𝜃) → (𝜒 ∧ 𝜏))) |
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