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Mirrors > Home > MPE Home > Th. List > Mathboxes > dalemqrprot | Structured version Visualization version Unicode version |
Description: Lemma for dath 33347. Frequently-used utility lemma. (Contributed by NM, 13-Aug-2012.) |
Ref | Expression |
---|---|
dalema.ph |
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dalemb.j |
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dalemb.a |
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Ref | Expression |
---|---|
dalemqrprot |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dalema.ph |
. . 3
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2 | 1 | dalemkehl 33234 |
. 2
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3 | 1 | dalemqea 33238 |
. 2
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4 | 1 | dalemrea 33239 |
. 2
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5 | 1 | dalempea 33237 |
. 2
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6 | dalemb.j |
. . 3
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7 | dalemb.a |
. . 3
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8 | 6, 7 | hlatjrot 32984 |
. 2
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9 | 2, 3, 4, 5, 8 | syl13anc 1278 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-8 1900 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-rep 4531 ax-sep 4541 ax-nul 4550 ax-pow 4598 ax-pr 4656 ax-un 6615 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-eu 2314 df-mo 2315 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-ral 2754 df-rex 2755 df-reu 2756 df-rab 2758 df-v 3059 df-sbc 3280 df-csb 3376 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-pw 3965 df-sn 3981 df-pr 3983 df-op 3987 df-uni 4213 df-iun 4294 df-br 4419 df-opab 4478 df-mpt 4479 df-id 4771 df-xp 4862 df-rel 4863 df-cnv 4864 df-co 4865 df-dm 4866 df-rn 4867 df-res 4868 df-ima 4869 df-iota 5569 df-fun 5607 df-fn 5608 df-f 5609 df-f1 5610 df-fo 5611 df-f1o 5612 df-fv 5613 df-riota 6282 df-ov 6323 df-oprab 6324 df-preset 16228 df-poset 16246 df-lub 16275 df-glb 16276 df-join 16277 df-meet 16278 df-lat 16347 df-ats 32879 df-atl 32910 df-cvlat 32934 df-hlat 32963 |
This theorem is referenced by: dalemrot 33268 dalemrotyz 33269 dalem6 33279 dalem7 33280 dalem11 33285 dalem12 33286 dalemrotps 33302 dalem30 33313 dalem35 33318 dalem58 33341 dalem59 33342 |
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