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Mirrors > Home > MPE Home > Th. List > qsex | Structured version Visualization version GIF version |
Description: A quotient set exists. (Contributed by NM, 14-Aug-1995.) |
Ref | Expression |
---|---|
qsex.1 | ⊢ 𝐴 ∈ V |
Ref | Expression |
---|---|
qsex | ⊢ (𝐴 / 𝑅) ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | qsex.1 | . 2 ⊢ 𝐴 ∈ V | |
2 | qsexg 8814 | . 2 ⊢ (𝐴 ∈ V → (𝐴 / 𝑅) ∈ V) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐴 / 𝑅) ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2106 Vcvv 3478 / cqs 8743 |
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 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-ext 2706 ax-rep 5285 |
This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1540 df-ex 1777 df-sb 2063 df-mo 2538 df-clab 2713 df-cleq 2727 df-clel 2814 df-rex 3069 df-v 3480 df-qs 8750 |
This theorem is referenced by: prjspval 42590 |
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