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Mirrors > Home > MPE Home > Th. List > axcontlem3 | Structured version Unicode version |
Description: Lemma for axcont 23394. Given the separation assumption, ![]() ![]() |
Ref | Expression |
---|---|
axcontlem3.1 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
axcontlem3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simplr2 1031 |
. 2
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2 | simpr2 995 |
. . . . . 6
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3 | 2 | anim1i 568 |
. . . . 5
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4 | simplr3 1032 |
. . . . . 6
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5 | 4 | adantr 465 |
. . . . 5
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6 | breq1 4406 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | opeq2 4171 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | 7 | breq2d 4415 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | 6, 8 | rspc2v 3186 |
. . . . 5
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10 | 3, 5, 9 | sylc 60 |
. . . 4
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11 | 10 | orcd 392 |
. . 3
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12 | 11 | ralrimiva 2830 |
. 2
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13 | axcontlem3.1 |
. . . 4
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14 | 13 | sseq2i 3492 |
. . 3
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15 | ssrab 3541 |
. . 3
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16 | 14, 15 | bitri 249 |
. 2
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17 | 1, 12, 16 | sylanbrc 664 |
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-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 |
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-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ral 2804 df-rab 2808 df-v 3080 df-dif 3442 df-un 3444 df-in 3446 df-ss 3453 df-nul 3749 df-if 3903 df-sn 3989 df-pr 3991 df-op 3995 df-br 4404 |
This theorem is referenced by: axcontlem9 23390 axcontlem10 23391 |
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