Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > atl0dm | Structured version Visualization version Unicode version |
Description: Condition necessary for zero element to exist. (Contributed by NM, 14-Sep-2018.) |
Ref | Expression |
---|---|
atl01dm.b | |
atl01dm.u | |
atl01dm.g |
Ref | Expression |
---|---|
atl0dm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | atl01dm.b | . . 3 | |
2 | atl01dm.g | . . 3 | |
3 | eqid 2622 | . . 3 | |
4 | eqid 2622 | . . 3 | |
5 | eqid 2622 | . . 3 | |
6 | 1, 2, 3, 4, 5 | isatl 34586 | . 2 |
7 | 6 | simp2bi 1077 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wcel 1990 wne 2794 wral 2912 wrex 2913 class class class wbr 4653 cdm 5114 cfv 5888 cbs 15857 cple 15948 club 16942 cglb 16943 cp0 17037 clat 17045 catm 34550 cal 34551 |
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 |
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-ne 2795 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-dm 5124 df-iota 5851 df-fv 5896 df-atl 34585 |
This theorem is referenced by: atl0cl 34590 atl0le 34591 |
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