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Mathbox for Peter Mazsa |
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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 8780 | . 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 1534 / cqs 8724 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-9 2109 ax-ext 2699 |
This theorem depends on definitions: df-bi 206 df-an 396 df-ex 1775 df-sb 2061 df-clab 2706 df-cleq 2720 df-rex 3068 df-qs 8731 |
This theorem is referenced by: dmqscoelseq 38133 |
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