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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > cdleme31sn1c | Structured version Visualization version Unicode version |
Description: Part of proof of Lemma E in [Crawley] p. 113. (Contributed by NM, 1-Mar-2013.) |
Ref | Expression |
---|---|
cdleme31sn1c.g |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
cdleme31sn1c.i |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
cdleme31sn1c.n |
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cdleme31sn1c.y |
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cdleme31sn1c.c |
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Ref | Expression |
---|---|
cdleme31sn1c |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdleme31sn1c.i |
. . 3
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2 | cdleme31sn1c.n |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | eqid 2471 |
. . 3
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4 | 1, 2, 3 | cdleme31sn1 34019 |
. 2
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5 | cdleme31sn1c.g |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | cdleme31sn1c.y |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 5, 6 | cdleme31se 34020 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | 7 | adantr 472 |
. . . . . . 7
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9 | 8 | eqeq2d 2481 |
. . . . . 6
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10 | 9 | imbi2d 323 |
. . . . 5
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11 | 10 | ralbidv 2829 |
. . . 4
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12 | 11 | riotabidv 6272 |
. . 3
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13 | cdleme31sn1c.c |
. . 3
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14 | 12, 13 | syl6eqr 2523 |
. 2
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15 | 4, 14 | eqtrd 2505 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ral 2761 df-rex 2762 df-rab 2765 df-v 3033 df-sbc 3256 df-csb 3350 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-sn 3960 df-pr 3962 df-op 3966 df-uni 4191 df-br 4396 df-iota 5553 df-fv 5597 df-riota 6270 df-ov 6311 |
This theorem is referenced by: cdlemefs32sn1aw 34052 cdleme43fsv1snlem 34058 cdleme41sn3a 34071 cdleme40m 34105 cdleme40n 34106 |
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