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Mirrors > Home > ILE Home > Th. List > qsex | 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 6632 | . 2 ⊢ (𝐴 ∈ V → (𝐴 / 𝑅) ∈ V) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐴 / 𝑅) ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2160 Vcvv 2756 / cqs 6573 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-coll 4140 ax-sep 4143 ax-pow 4199 ax-pr 4234 ax-un 4458 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-reu 2475 df-rab 2477 df-v 2758 df-sbc 2982 df-csb 3077 df-un 3153 df-in 3155 df-ss 3162 df-pw 3599 df-sn 3620 df-pr 3621 df-op 3623 df-uni 3832 df-iun 3910 df-br 4026 df-opab 4087 df-mpt 4088 df-id 4318 df-xp 4657 df-rel 4658 df-cnv 4659 df-co 4660 df-dm 4661 df-rn 4662 df-res 4663 df-ima 4664 df-iota 5203 df-fun 5244 df-fn 5245 df-f 5246 df-f1 5247 df-fo 5248 df-f1o 5249 df-fv 5250 df-qs 6580 |
This theorem is referenced by: nqex 7409 nq0ex 7486 addvalex 7890 |
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