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Mirrors > Home > HSE Home > Th. List > cmbri | Structured version Visualization version Unicode version |
Description: Binary relation expressing the commutes relation. Definition of commutes in [Kalmbach] p. 20. (Contributed by NM, 6-Aug-2004.) (New usage is discouraged.) |
Ref | Expression |
---|---|
pjoml2.1 | |
pjoml2.2 |
Ref | Expression |
---|---|
cmbri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pjoml2.1 | . 2 | |
2 | pjoml2.2 | . 2 | |
3 | cmbr 28443 | . 2 | |
4 | 1, 2, 3 | mp2an 708 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wceq 1483 wcel 1990 cin 3573 class class class wbr 4653 cfv 5888 (class class class)co 6650 cch 27786 cort 27787 chj 27790 ccm 27793 |
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-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-iota 5851 df-fv 5896 df-ov 6653 df-cm 28442 |
This theorem is referenced by: cmcmlem 28450 cmcm2i 28452 cmbr2i 28455 cmbr3i 28459 pjclem1 29054 pjci 29059 |
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