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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > dalempjqeb | Structured version Visualization version Unicode version |
Description: Lemma for dath 33303. 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 |
---|---|
dalempjqeb |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dalema.ph |
. . 3
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2 | 1 | dalemkehl 33190 |
. 2
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3 | 1 | dalempea 33193 |
. 2
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4 | 1 | dalemqea 33194 |
. 2
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5 | eqid 2452 |
. . 3
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6 | dalemb.j |
. . 3
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7 | dalemb.a |
. . 3
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8 | 5, 6, 7 | hlatjcl 32934 |
. 2
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9 | 2, 3, 4, 8 | syl3anc 1271 |
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-8 1893 ax-9 1900 ax-10 1919 ax-11 1924 ax-12 1937 ax-13 2092 ax-ext 2432 ax-rep 4487 ax-sep 4497 ax-nul 4506 ax-pow 4554 ax-pr 4612 ax-un 6571 |
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-ral 2742 df-rex 2743 df-reu 2744 df-rab 2746 df-v 3015 df-sbc 3236 df-csb 3332 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-uni 4169 df-iun 4250 df-br 4375 df-opab 4434 df-mpt 4435 df-id 4727 df-xp 4818 df-rel 4819 df-cnv 4820 df-co 4821 df-dm 4822 df-rn 4823 df-res 4824 df-ima 4825 df-iota 5525 df-fun 5563 df-fn 5564 df-f 5565 df-f1 5566 df-fo 5567 df-f1o 5568 df-fv 5569 df-riota 6238 df-ov 6279 df-oprab 6280 df-lub 16231 df-glb 16232 df-join 16233 df-meet 16234 df-lat 16303 df-ats 32835 df-atl 32866 df-cvlat 32890 df-hlat 32919 |
This theorem is referenced by: dalemcea 33227 dalem3 33231 dalem4 33232 dalem5 33234 dalem-cly 33238 dalem10 33240 dalem17 33247 dalem38 33277 dalem44 33283 dalem48 33287 dalem54 33293 dalem55 33294 dalem57 33296 |
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