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Mirrors > Home > MPE Home > Th. List > difprsn1 | Structured version 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 2717 |
. 2
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2 | disjsn2 4035 |
. . . 4
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3 | disj3 3821 |
. . . 4
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4 | 2, 3 | sylib 196 |
. . 3
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5 | df-pr 3978 |
. . . . . 6
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6 | 5 | equncomi 3600 |
. . . . 5
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7 | 6 | difeq1i 3568 |
. . . 4
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8 | difun2 3856 |
. . . 4
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9 | 7, 8 | eqtri 2480 |
. . 3
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10 | 4, 9 | syl6reqr 2511 |
. 2
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11 | 1, 10 | sylbir 213 |
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 1952 ax-ext 2430 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ne 2646 df-ral 2800 df-rab 2804 df-v 3070 df-dif 3429 df-un 3431 df-in 3433 df-ss 3440 df-nul 3736 df-sn 3976 df-pr 3978 |
This theorem is referenced by: difprsn2 4109 pmtrprfval 16095 usgra1v 23443 cusgra2v 23505 eulerpartlemgf 26896 coinflippvt 27001 f12dfv 30284 frgra2v 30729 ldepsnlinc 31157 |
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