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Mirrors > Home > MPE Home > Th. List > fnresi | Structured version Visualization version Unicode version |
Description: Functionality and domain of restricted identity. (Contributed by NM, 27-Aug-2004.) |
Ref | Expression |
---|---|
fnresi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funi 5920 | . . 3 | |
2 | funres 5929 | . . 3 | |
3 | 1, 2 | ax-mp 5 | . 2 |
4 | dmresi 5457 | . 2 | |
5 | df-fn 5891 | . 2 | |
6 | 3, 4, 5 | mpbir2an 955 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 cid 5023 cdm 5114 cres 5116 wfun 5882 wfn 5883 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-res 5126 df-fun 5890 df-fn 5891 |
This theorem is referenced by: idssxp 6009 f1oi 6174 fninfp 6440 fndifnfp 6442 fnnfpeq0 6444 fveqf1o 6557 weniso 6604 iordsmo 7454 fipreima 8272 dfac9 8958 pmtrfinv 17881 ustuqtop3 22047 fta1blem 23928 qaa 24078 dfiop2 28612 cvmliftlem4 31270 cvmliftlem5 31271 poimirlem15 33424 poimirlem22 33431 ltrnid 35421 rtrclex 37924 dvsid 38530 dflinc2 42199 |
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