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Mirrors > Home > ILE Home > Th. List > difprsn1 | Unicode version |
Description: Removal of a singleton from an unordered pair. (Contributed by Thierry Arnoux, 4-Feb-2017.) |
Ref | Expression |
---|---|
difprsn1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | necom 2431 |
. 2
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2 | df-pr 3598 |
. . . . . 6
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3 | 2 | equncomi 3281 |
. . . . 5
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4 | 3 | difeq1i 3249 |
. . . 4
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5 | difun2 3502 |
. . . 4
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6 | 4, 5 | eqtri 2198 |
. . 3
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7 | disjsn2 3654 |
. . . 4
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8 | disj3 3475 |
. . . 4
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9 | 7, 8 | sylib 122 |
. . 3
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10 | 6, 9 | eqtr4id 2229 |
. 2
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11 | 1, 10 | sylbir 135 |
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 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-ral 2460 df-rab 2464 df-v 2739 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-nul 3423 df-sn 3597 df-pr 3598 |
This theorem is referenced by: difprsn2 3731 |
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