![]() |
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 8715 | . 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 2107 Vcvv 3446 / cqs 8648 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2708 ax-rep 5243 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-sb 2069 df-mo 2539 df-clab 2715 df-cleq 2729 df-clel 2815 df-ral 3066 df-rex 3075 df-v 3448 df-qs 8655 |
This theorem is referenced by: prjspval 40944 |
Copyright terms: Public domain | W3C validator |