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Mirrors > Home > MPE Home > Th. List > domnsym | Structured version Visualization version Unicode version |
Description: Theorem 22(i) of [Suppes] p. 97. (Contributed by NM, 10-Jun-1998.) |
Ref | Expression |
---|---|
domnsym |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | brdom2 7985 | . 2 | |
2 | sdomnsym 8085 | . . 3 | |
3 | sdomnen 7984 | . . . 4 | |
4 | ensym 8005 | . . . 4 | |
5 | 3, 4 | nsyl3 133 | . . 3 |
6 | 2, 5 | jaoi 394 | . 2 |
7 | 1, 6 | sylbi 207 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wo 383 class class class wbr 4653 cen 7952 cdom 7953 csdm 7954 |
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-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-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-res 5126 df-ima 5127 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-er 7742 df-en 7956 df-dom 7957 df-sdom 7958 |
This theorem is referenced by: sdom0 8092 sdomdomtr 8093 domsdomtr 8095 sdomdif 8108 onsdominel 8109 nndomo 8154 sdom1 8160 fofinf1o 8241 carddom2 8803 fidomtri 8819 fidomtri2 8820 infxpenlem 8836 alephordi 8897 infdif 9031 infdif2 9032 cfslbn 9089 cfslb2n 9090 fincssdom 9145 fin45 9214 domtriom 9265 alephval2 9394 alephreg 9404 pwcfsdom 9405 cfpwsdom 9406 pwfseqlem3 9482 gchpwdom 9492 gchaleph 9493 hargch 9495 gchhar 9501 winainflem 9515 rankcf 9599 tskcard 9603 vdwlem12 15696 odinf 17980 rectbntr0 22635 erdszelem10 31182 finminlem 32312 fphpd 37380 |
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