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Mirrors > Home > HSE Home > Th. List > cvnbtwn | Structured version Visualization version Unicode version |
Description: The covers relation implies no in-betweenness. (Contributed by NM, 12-Jun-2004.) (New usage is discouraged.) |
Ref | Expression |
---|---|
cvnbtwn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cvbr 27935 |
. . . 4
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2 | psseq2 3521 |
. . . . . . . . 9
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3 | psseq1 3520 |
. . . . . . . . 9
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4 | 2, 3 | anbi12d 717 |
. . . . . . . 8
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5 | 4 | rspcev 3150 |
. . . . . . 7
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6 | 5 | ex 436 |
. . . . . 6
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7 | 6 | con3rr3 142 |
. . . . 5
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8 | 7 | adantl 468 |
. . . 4
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9 | 1, 8 | syl6bi 232 |
. . 3
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10 | 9 | com23 81 |
. 2
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11 | 10 | 3impia 1205 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-sep 4525 ax-nul 4534 ax-pr 4639 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-rex 2743 df-rab 2746 df-v 3047 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-pss 3420 df-nul 3732 df-if 3882 df-sn 3969 df-pr 3971 df-op 3975 df-br 4403 df-opab 4462 df-cv 27932 |
This theorem is referenced by: cvnbtwn2 27940 cvnbtwn3 27941 cvnbtwn4 27942 cvntr 27945 |
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