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Mirrors > Home > MPE Home > Th. List > coeq2d | Structured version Visualization version GIF version |
Description: Equality deduction for composition of two classes. (Contributed by NM, 16-Nov-2000.) |
Ref | Expression |
---|---|
coeq1d.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
Ref | Expression |
---|---|
coeq2d | ⊢ (𝜑 → (𝐶 ∘ 𝐴) = (𝐶 ∘ 𝐵)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | coeq1d.1 | . 2 ⊢ (𝜑 → 𝐴 = 𝐵) | |
2 | coeq2 5727 | . 2 ⊢ (𝐴 = 𝐵 → (𝐶 ∘ 𝐴) = (𝐶 ∘ 𝐵)) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝐶 ∘ 𝐴) = (𝐶 ∘ 𝐵)) |
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