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Mirrors > Home > MPE Home > Th. List > mhmf | Structured version Visualization version Unicode version |
Description: A monoid homomorphism is a function. (Contributed by Mario Carneiro, 7-Mar-2015.) |
Ref | Expression |
---|---|
mhmf.b | |
mhmf.c |
Ref | Expression |
---|---|
mhmf | MndHom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mhmf.b | . . . 4 | |
2 | mhmf.c | . . . 4 | |
3 | eqid 2622 | . . . 4 | |
4 | eqid 2622 | . . . 4 | |
5 | eqid 2622 | . . . 4 | |
6 | eqid 2622 | . . . 4 | |
7 | 1, 2, 3, 4, 5, 6 | ismhm 17337 | . . 3 MndHom |
8 | 7 | simprbi 480 | . 2 MndHom |
9 | 8 | simp1d 1073 | 1 MndHom |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wceq 1483 wcel 1990 wral 2912 wf 5884 cfv 5888 (class class class)co 6650 cbs 15857 cplusg 15941 c0g 16100 cmnd 17294 MndHom cmhm 17333 |
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-8 1992 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-pow 4843 ax-pr 4906 ax-un 6949 |
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-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 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-rn 5125 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-map 7859 df-mhm 17335 |
This theorem is referenced by: mhmf1o 17345 resmhm 17359 resmhm2 17360 resmhm2b 17361 mhmco 17362 mhmima 17363 mhmeql 17364 pwsco2mhm 17371 gsumwmhm 17382 frmdup3lem 17403 frmdup3 17404 mhmmulg 17583 ghmmhmb 17671 cntzmhm 17771 cntzmhm2 17772 frgpup3lem 18190 gsumzmhm 18337 gsummhm2 18339 gsummptmhm 18340 mhmvlin 20203 mdetleib2 20394 mdetf 20401 mdetdiaglem 20404 mdetrlin 20408 mdetrsca 20409 mdetralt 20414 mdetunilem7 20424 mdetunilem8 20425 dchrelbas2 24962 dchrn0 24975 mhmhmeotmd 29973 |
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