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Mirrors > Home > MPE Home > Th. List > elfz1 | Structured version Visualization version Unicode version |
Description: Membership in a finite set of sequential integers. (Contributed by NM, 21-Jul-2005.) |
Ref | Expression |
---|---|
elfz1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fzval 12328 | . . 3 | |
2 | 1 | eleq2d 2687 | . 2 |
3 | breq2 4657 | . . . . 5 | |
4 | breq1 4656 | . . . . 5 | |
5 | 3, 4 | anbi12d 747 | . . . 4 |
6 | 5 | elrab 3363 | . . 3 |
7 | 3anass 1042 | . . 3 | |
8 | 6, 7 | bitr4i 267 | . 2 |
9 | 2, 8 | syl6bb 276 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wceq 1483 wcel 1990 crab 2916 class class class wbr 4653 (class class class)co 6650 cle 10075 cz 11377 cfz 12326 |
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 ax-cnex 9992 ax-resscn 9993 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 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-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-iota 5851 df-fun 5890 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-neg 10269 df-z 11378 df-fz 12327 |
This theorem is referenced by: elfz 12332 elfz2 12333 fzen 12358 fzaddel 12375 fzadd2 12376 elfzm11 12411 fznn0 12432 phicl2 15473 nndiffz1 29548 fzmul 33537 fz1eqin 37332 jm2.27dlem2 37577 iblspltprt 40189 itgspltprt 40195 |
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