![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 8787 | . 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 2099 Vcvv 3470 / cqs 8717 |
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-8 2101 ax-9 2109 ax-ext 2699 ax-rep 5279 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1537 df-ex 1775 df-sb 2061 df-mo 2530 df-clab 2706 df-cleq 2720 df-clel 2806 df-rex 3067 df-v 3472 df-qs 8724 |
This theorem is referenced by: prjspval 42021 |
Copyright terms: Public domain | W3C validator |