Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > dmex | GIF version |
Description: The domain of a set is a set. Corollary 6.8(2) of [TakeutiZaring] p. 26. (Contributed by NM, 7-Jul-2008.) |
Ref | Expression |
---|---|
dmex.1 | ⊢ 𝐴 ∈ V |
Ref | Expression |
---|---|
dmex | ⊢ dom 𝐴 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmex.1 | . 2 ⊢ 𝐴 ∈ V | |
2 | dmexg 4773 | . 2 ⊢ (𝐴 ∈ V → dom 𝐴 ∈ V) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ dom 𝐴 ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1465 Vcvv 2660 dom cdm 4509 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-un 4325 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-cnv 4517 df-dm 4519 df-rn 4520 |
This theorem is referenced by: ofmres 6002 fo1st 6023 tfrlem8 6183 rdgtfr 6239 rdgruledefgg 6240 rdgon 6251 mapprc 6514 ixpprc 6581 ixpssmap2g 6589 ixpssmapg 6590 bren 6609 brdomg 6610 fundmen 6668 xpassen 6692 mapen 6708 ssenen 6713 hashfacen 10547 shftfval 10561 |
Copyright terms: Public domain | W3C validator |