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Mirrors > Home > MPE Home > Th. List > Mathboxes > 4atlem0ae | Structured version Unicode version |
Description: Lemma for 4at 33563. (Contributed by NM, 10-Jul-2012.) |
Ref | Expression |
---|---|
4at.l |
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4at.j |
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4at.a |
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Ref | Expression |
---|---|
4atlem0ae |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp3r 1017 |
. 2
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2 | simp1 988 |
. . 3
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3 | simp22 1022 |
. . 3
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4 | simp23 1023 |
. . 3
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5 | simp21 1021 |
. . 3
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6 | simp3l 1016 |
. . . 4
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7 | 6 | necomd 2719 |
. . 3
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8 | 4at.l |
. . . 4
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9 | 4at.j |
. . . 4
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10 | 4at.a |
. . . 4
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11 | 8, 9, 10 | hlatexch1 33345 |
. . 3
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12 | 2, 3, 4, 5, 7, 11 | syl131anc 1232 |
. 2
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13 | 1, 12 | mtod 177 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-8 1760 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 ax-rep 4501 ax-sep 4511 ax-nul 4519 ax-pow 4568 ax-pr 4629 ax-un 6472 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2264 df-mo 2265 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ne 2646 df-ral 2800 df-rex 2801 df-reu 2802 df-rab 2804 df-v 3070 df-sbc 3285 df-csb 3387 df-dif 3429 df-un 3431 df-in 3433 df-ss 3440 df-nul 3736 df-if 3890 df-pw 3960 df-sn 3976 df-pr 3978 df-op 3982 df-uni 4190 df-iun 4271 df-br 4391 df-opab 4449 df-mpt 4450 df-id 4734 df-xp 4944 df-rel 4945 df-cnv 4946 df-co 4947 df-dm 4948 df-rn 4949 df-res 4950 df-ima 4951 df-iota 5479 df-fun 5518 df-fn 5519 df-f 5520 df-f1 5521 df-fo 5522 df-f1o 5523 df-fv 5524 df-riota 6151 df-ov 6193 df-oprab 6194 df-poset 15218 df-plt 15230 df-lub 15246 df-glb 15247 df-join 15248 df-meet 15249 df-p0 15311 df-lat 15318 df-covers 33217 df-ats 33218 df-atl 33249 df-cvlat 33273 df-hlat 33302 |
This theorem is referenced by: 4atlem11 33559 2llnma2 33739 4atexlemc 34019 |
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