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Mirrors > Home > MPE Home > Th. List > dmmptss | Structured version Visualization version Unicode version |
Description: The domain of a mapping is a subset of its base class. (Contributed by Scott Fenton, 17-Jun-2013.) |
Ref | Expression |
---|---|
dmmpt.1 |
Ref | Expression |
---|---|
dmmptss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmmpt.1 | . . 3 | |
2 | 1 | dmmpt 5630 | . 2 |
3 | ssrab2 3687 | . 2 | |
4 | 2, 3 | eqsstri 3635 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 wcel 1990 crab 2916 cvv 3200 wss 3574 cmpt 4729 cdm 5114 |
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-xp 5120 df-rel 5121 df-cnv 5122 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 |
This theorem is referenced by: mptrcl 6289 fvmptss 6292 fvmptex 6294 fvmptnf 6302 elfvmptrab1 6305 mptexg 6484 dmmpt2ssx 7235 curry1val 7270 curry2val 7274 tposssxp 7356 mptfi 8265 cnvimamptfin 8267 cantnfres 8574 mptct 9360 bitsval 15146 subcrcl 16476 arwval 16693 arwrcl 16694 coafval 16714 submrcl 17346 issubg 17594 isnsg 17623 cntzrcl 17760 gsumconst 18334 abvrcl 18821 psrass1lem 19377 psrass1 19405 psrass23l 19408 psrcom 19409 psrass23 19410 mpfrcl 19518 psropprmul 19608 coe1mul2 19639 isobs 20064 lmrcl 21035 1stcrestlem 21255 islocfin 21320 kgeni 21340 ptbasfi 21384 isxms2 22253 setsmstopn 22283 tngtopn 22454 isphtpc 22793 pcofval 22810 cfili 23066 cfilfcls 23072 rrxmval 23188 plybss 23950 ulmss 24151 dchrrcl 24965 gsummpt2co 29780 locfinreflem 29907 sitgclg 30404 cvmsrcl 31246 snmlval 31313 eldiophb 37320 elmnc 37706 itgocn 37734 issdrg 37767 submgmrcl 41782 dmmpt2ssx2 42115 |
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