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Mirrors > Home > MPE Home > Th. List > Mathboxes > clcllaw | Structured version Visualization version Unicode version |
Description: Closure of a closed operation. (Contributed by FL, 14-Sep-2010.) (Revised by AV, 21-Jan-2020.) |
Ref | Expression |
---|---|
clcllaw | clLaw |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-cllaw 41822 | . . . 4 clLaw | |
2 | 1 | bropaex12 5192 | . . 3 clLaw |
3 | iscllaw 41825 | . . . 4 clLaw | |
4 | ovrspc2v 6672 | . . . . 5 | |
5 | 4 | expcom 451 | . . . 4 |
6 | 3, 5 | syl6bi 243 | . . 3 clLaw |
7 | 2, 6 | mpcom 38 | . 2 clLaw |
8 | 7 | 3impib 1262 | 1 clLaw |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wcel 1990 wral 2912 cvv 3200 class class class wbr 4653 (class class class)co 6650 clLaw ccllaw 41819 |
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-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-iota 5851 df-fv 5896 df-ov 6653 df-cllaw 41822 |
This theorem is referenced by: (None) |
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