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Mirrors > Home > ILE Home > Th. List > opeq2d | Unicode version |
Description: Equality deduction for ordered pairs. (Contributed by NM, 16-Dec-2006.) |
Ref | Expression |
---|---|
opeq1d.1 |
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Ref | Expression |
---|---|
opeq2d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opeq1d.1 |
. 2
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2 | opeq2 3714 |
. 2
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3 | 1, 2 | syl 14 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-sn 3538 df-pr 3539 df-op 3541 |
This theorem is referenced by: tfr1onlemaccex 6253 tfrcllemaccex 6266 fundmen 6708 recexnq 7222 suplocexprlemex 7554 elreal2 7662 frecuzrdgrrn 10212 frec2uzrdg 10213 frecuzrdgrcl 10214 frecuzrdgsuc 10218 frecuzrdgrclt 10219 frecuzrdgg 10220 frecuzrdgsuctlem 10227 seqeq2 10253 seqeq3 10254 iseqvalcbv 10261 seq3val 10262 seqvalcd 10263 eucalgval 11771 ennnfonelemp1 11955 ennnfonelemnn0 11971 strsetsid 12031 ressid2 12057 ressval2 12058 |
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