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Mirrors > Home > MPE Home > Th. List > Mathboxes > qseq1i | Structured version Visualization version GIF version |
Description: Equality theorem for quotient set, inference form. (Contributed by Peter Mazsa, 3-Jun-2021.) |
Ref | Expression |
---|---|
qseq1i.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
qseq1i | ⊢ (𝐴 / 𝐶) = (𝐵 / 𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | qseq1i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | qseq1 8337 | . 2 ⊢ (𝐴 = 𝐵 → (𝐴 / 𝐶) = (𝐵 / 𝐶)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐴 / 𝐶) = (𝐵 / 𝐶) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 / cqs 8282 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1777 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-rex 3144 df-qs 8289 |
This theorem is referenced by: dmqscoelseq 35889 |
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