Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > dfer2 | Structured version Visualization version Unicode version |
Description: Alternate definition of equivalence predicate. (Contributed by NM, 3-Jan-1997.) (Revised by Mario Carneiro, 12-Aug-2015.) |
Ref | Expression |
---|---|
dfer2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-er 7742 | . 2 | |
2 | cnvsym 5510 | . . . . 5 | |
3 | cotr 5508 | . . . . 5 | |
4 | 2, 3 | anbi12i 733 | . . . 4 |
5 | unss 3787 | . . . 4 | |
6 | 19.28v 1909 | . . . . . . . 8 | |
7 | 6 | albii 1747 | . . . . . . 7 |
8 | 19.26 1798 | . . . . . . 7 | |
9 | 7, 8 | bitri 264 | . . . . . 6 |
10 | 9 | albii 1747 | . . . . 5 |
11 | 19.26 1798 | . . . . 5 | |
12 | 10, 11 | bitr2i 265 | . . . 4 |
13 | 4, 5, 12 | 3bitr3i 290 | . . 3 |
14 | 13 | 3anbi3i 1255 | . 2 |
15 | 1, 14 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wal 1481 wceq 1483 cun 3572 wss 3574 class class class wbr 4653 ccnv 5113 cdm 5114 ccom 5118 wrel 5119 wer 7739 |
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-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-br 4654 df-opab 4713 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-er 7742 |
This theorem is referenced by: iserd 7768 trer 32310 riscer 33787 prter1 34164 |
Copyright terms: Public domain | W3C validator |