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Mirrors > Home > ILE Home > Th. List > 2onetap | Unicode version |
Description: Negated equality is a
tight apartness on ![]() |
Ref | Expression |
---|---|
2onetap |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2onn 6569 |
. . . . 5
![]() ![]() ![]() ![]() | |
2 | elnn 4636 |
. . . . 5
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3 | 1, 2 | mpan2 425 |
. . . 4
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4 | elnn 4636 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 1, 4 | mpan2 425 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | nndceq 6547 |
. . . 4
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7 | 3, 5, 6 | syl2an 289 |
. . 3
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8 | 7 | rgen2 2580 |
. 2
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9 | netap 7308 |
. 2
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10 | 8, 9 | ax-mp 5 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2166 ax-14 2167 ax-ext 2175 ax-sep 4147 ax-nul 4155 ax-pow 4203 ax-pr 4238 ax-un 4462 ax-setind 4567 ax-iinf 4618 |
This theorem depends on definitions: df-bi 117 df-dc 836 df-3or 981 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2045 df-mo 2046 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-ne 2365 df-ral 2477 df-rex 2478 df-v 2762 df-dif 3155 df-un 3157 df-in 3159 df-ss 3166 df-nul 3447 df-pw 3603 df-sn 3624 df-pr 3625 df-op 3627 df-uni 3836 df-int 3871 df-br 4030 df-opab 4091 df-tr 4128 df-iord 4395 df-on 4397 df-suc 4400 df-iom 4621 df-xp 4663 df-1o 6464 df-2o 6465 df-pap 7302 df-tap 7304 |
This theorem is referenced by: 2omotaplemst 7312 |
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