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Mirrors > Home > MPE Home > Th. List > isuslgra | Structured version Visualization version Unicode version |
Description: The property of being an undirected simple graph with loops. (Contributed by Alexander van der Vekens, 10-Aug-2017.) |
Ref | Expression |
---|---|
isuslgra |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1eq1 5757 |
. . . 4
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2 | 1 | adantl 472 |
. . 3
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3 | dmeq 5013 |
. . . . 5
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4 | 3 | adantl 472 |
. . . 4
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5 | f1eq2 5758 |
. . . 4
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6 | 4, 5 | syl 17 |
. . 3
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7 | simpl 463 |
. . . . . 6
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8 | 7 | pweqd 3924 |
. . . . 5
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9 | 8 | difeq1d 3518 |
. . . 4
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10 | rabeq 3006 |
. . . 4
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11 | f1eq3 5759 |
. . . 4
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12 | 9, 10, 11 | 3syl 18 |
. . 3
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13 | 2, 6, 12 | 3bitrd 287 |
. 2
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14 | df-uslgra 25071 |
. 2
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15 | 13, 14 | brabga 4688 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1673 ax-4 1686 ax-5 1762 ax-6 1809 ax-7 1855 ax-9 1900 ax-10 1919 ax-11 1924 ax-12 1937 ax-13 2092 ax-ext 2432 ax-sep 4497 ax-nul 4506 ax-pr 4612 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 988 df-tru 1451 df-ex 1668 df-nf 1672 df-sb 1802 df-eu 2304 df-mo 2305 df-clab 2439 df-cleq 2445 df-clel 2448 df-nfc 2582 df-ne 2624 df-rab 2746 df-v 3015 df-dif 3375 df-un 3377 df-in 3379 df-ss 3386 df-nul 3700 df-if 3850 df-pw 3921 df-sn 3937 df-pr 3939 df-op 3943 df-br 4375 df-opab 4434 df-rel 4819 df-cnv 4820 df-co 4821 df-dm 4822 df-rn 4823 df-fun 5563 df-fn 5564 df-f 5565 df-f1 5566 df-uslgra 25071 |
This theorem is referenced by: uslgraf 25084 uslisushgra 25102 uslisumgra 25103 usisuslgra 25104 uslgra1 25111 |
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