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Mirrors > Home > MPE Home > Th. List > isfin5 | Structured version Visualization version Unicode version |
Description: Definition of a V-finite set. (Contributed by Stefan O'Rear, 16-May-2015.) |
Ref | Expression |
---|---|
isfin5 | FinV |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-fin5 9111 | . . 3 FinV | |
2 | 1 | eleq2i 2693 | . 2 FinV |
3 | id 22 | . . . . 5 | |
4 | 0ex 4790 | . . . . 5 | |
5 | 3, 4 | syl6eqel 2709 | . . . 4 |
6 | relsdom 7962 | . . . . 5 | |
7 | 6 | brrelexi 5158 | . . . 4 |
8 | 5, 7 | jaoi 394 | . . 3 |
9 | eqeq1 2626 | . . . 4 | |
10 | id 22 | . . . . 5 | |
11 | 10, 10 | oveq12d 6668 | . . . . 5 |
12 | 10, 11 | breq12d 4666 | . . . 4 |
13 | 9, 12 | orbi12d 746 | . . 3 |
14 | 8, 13 | elab3 3358 | . 2 |
15 | 2, 14 | bitri 264 | 1 FinV |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wo 383 wceq 1483 wcel 1990 cab 2608 cvv 3200 c0 3915 class class class wbr 4653 (class class class)co 6650 csdm 7954 ccda 8989 FinVcfin5 9104 |
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-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-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-xp 5120 df-rel 5121 df-iota 5851 df-fv 5896 df-ov 6653 df-dom 7957 df-sdom 7958 df-fin5 9111 |
This theorem is referenced by: isfin5-2 9213 fin56 9215 |
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