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Mirrors > Home > ILE Home > Th. List > difprsnss | Unicode version |
Description: Removal of a singleton from an unordered pair. (Contributed by NM, 16-Mar-2006.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) |
Ref | Expression |
---|---|
difprsnss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2615 |
. . . . 5
![]() ![]() ![]() ![]() | |
2 | 1 | elpr 3443 |
. . . 4
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3 | velsn 3439 |
. . . . 5
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4 | 3 | notbii 627 |
. . . 4
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5 | biorf 696 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | 5 | biimparc 293 |
. . . 4
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7 | 2, 4, 6 | syl2anb 285 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | eldif 2993 |
. . 3
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9 | velsn 3439 |
. . 3
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10 | 7, 8, 9 | 3imtr4i 199 |
. 2
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11 | 10 | ssriv 3014 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-v 2614 df-dif 2986 df-un 2988 df-in 2990 df-ss 2997 df-sn 3428 df-pr 3429 |
This theorem is referenced by: en2other2 6725 |
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