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Mirrors > Home > MPE Home > Th. List > funimass3 | Structured version Visualization version Unicode version |
Description: A kind of contraposition law that infers an image subclass from a subclass of a preimage. Raph Levien remarks: "Likely this could be proved directly, and fvimacnv 6332 would be the special case of being a singleton, but it works this way round too." (Contributed by Raph Levien, 20-Nov-2006.) |
Ref | Expression |
---|---|
funimass3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funimass4 6247 | . . 3 | |
2 | ssel 3597 | . . . . . 6 | |
3 | fvimacnv 6332 | . . . . . . 7 | |
4 | 3 | ex 450 | . . . . . 6 |
5 | 2, 4 | syl9r 78 | . . . . 5 |
6 | 5 | imp31 448 | . . . 4 |
7 | 6 | ralbidva 2985 | . . 3 |
8 | 1, 7 | bitrd 268 | . 2 |
9 | dfss3 3592 | . 2 | |
10 | 8, 9 | syl6bbr 278 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wcel 1990 wral 2912 wss 3574 ccnv 5113 cdm 5114 cima 5117 wfun 5882 cfv 5888 |
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-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-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-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-fv 5896 |
This theorem is referenced by: funimass5 6334 funconstss 6335 fvimacnvALT 6336 fimacnv 6347 r0weon 8835 iscnp3 21048 cnpnei 21068 cnclsi 21076 cncls 21078 cncnp 21084 1stccnp 21265 txcnpi 21411 xkoco2cn 21461 xkococnlem 21462 basqtop 21514 kqnrmlem1 21546 kqnrmlem2 21547 reghmph 21596 nrmhmph 21597 elfm3 21754 rnelfm 21757 symgtgp 21905 tgpconncompeqg 21915 eltsms 21936 ucnprima 22086 plyco0 23948 plyeq0 23967 xrlimcnp 24695 rinvf1o 29432 xppreima 29449 cvmliftmolem1 31263 cvmlift2lem9 31293 cvmlift3lem6 31306 mclsppslem 31480 |
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