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Mirrors > Home > MPE Home > Th. List > Mathboxes > qseq1d | Structured version Visualization version GIF version |
Description: Equality theorem for quotient set, deduction form. (Contributed by Peter Mazsa, 27-May-2021.) |
Ref | Expression |
---|---|
qseq1d.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
Ref | Expression |
---|---|
qseq1d | ⊢ (𝜑 → (𝐴 / 𝐶) = (𝐵 / 𝐶)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | qseq1d.1 | . 2 ⊢ (𝜑 → 𝐴 = 𝐵) | |
2 | qseq1 8345 | . 2 ⊢ (𝐴 = 𝐵 → (𝐴 / 𝐶) = (𝐵 / 𝐶)) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝐴 / 𝐶) = (𝐵 / 𝐶)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1537 / cqs 8290 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-ext 2795 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1781 df-sb 2070 df-clab 2802 df-cleq 2816 df-clel 2895 df-rex 3146 df-qs 8297 |
This theorem is referenced by: n0el3 35887 |
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