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Mirrors > Home > MPE Home > Th. List > funmpt2 | Structured version Visualization version Unicode version |
Description: Functionality of a class given by a "maps to" notation. (Contributed by FL, 17-Feb-2008.) (Revised by Mario Carneiro, 31-May-2014.) |
Ref | Expression |
---|---|
funmpt2.1 |
Ref | Expression |
---|---|
funmpt2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funmpt 5926 | . 2 | |
2 | funmpt2.1 | . . 3 | |
3 | 2 | funeqi 5909 | . 2 |
4 | 1, 3 | mpbir 221 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 cmpt 4729 wfun 5882 |
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-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-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-fun 5890 |
This theorem is referenced by: cantnfp1lem1 8575 tz9.12lem2 8651 tz9.12lem3 8652 rankf 8657 cardf2 8769 fin23lem30 9164 hashf1rn 13142 hashf1rnOLD 13143 funtopon 20725 qustgpopn 21923 ustn0 22024 metuval 22354 ipasslem8 27692 xppreima2 29450 funcnvmpt 29468 gsummpt2co 29780 metidval 29933 pstmval 29938 brsiga 30246 measbasedom 30265 sseqval 30450 ballotlem7 30597 sinccvglem 31566 bj-evalfun 33025 bj-ccinftydisj 33100 bj-elccinfty 33101 bj-minftyccb 33112 comptiunov2i 37998 icccncfext 40100 stoweidlem27 40244 stirlinglem14 40304 fourierdlem70 40393 fourierdlem71 40394 hoi2toco 40821 mptcfsupp 42161 lcoc0 42211 lincresunit2 42267 |
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