Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > dmmpt | Unicode version |
Description: The domain of the mapping operation in general. (Contributed by NM, 16-May-1995.) (Revised by Mario Carneiro, 22-Mar-2015.) |
Ref | Expression |
---|---|
dmmpo.1 |
Ref | Expression |
---|---|
dmmpt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfdm4 4778 | . 2 | |
2 | dfrn4 5046 | . 2 | |
3 | dmmpo.1 | . . 3 | |
4 | 3 | mptpreima 5079 | . 2 |
5 | 1, 2, 4 | 3eqtri 2182 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1335 wcel 2128 crab 2439 cvv 2712 cmpt 4025 ccnv 4585 cdm 4586 crn 4587 cima 4589 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-rab 2444 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-br 3966 df-opab 4026 df-mpt 4027 df-xp 4592 df-rel 4593 df-cnv 4594 df-dm 4596 df-rn 4597 df-res 4598 df-ima 4599 |
This theorem is referenced by: dmmptss 5082 dmmptg 5083 dmmptd 5300 fvmptssdm 5552 isnumi 7117 dvrecap 13077 |
Copyright terms: Public domain | W3C validator |