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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 |
Ref | Expression |
---|---|
opeq2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opeq1d.1 | . 2 | |
2 | opeq2 3676 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 cop 3500 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 df-op 3506 |
This theorem is referenced by: tfr1onlemaccex 6213 tfrcllemaccex 6226 fundmen 6668 recexnq 7166 suplocexprlemex 7498 elreal2 7606 frecuzrdgrrn 10149 frec2uzrdg 10150 frecuzrdgrcl 10151 frecuzrdgsuc 10155 frecuzrdgrclt 10156 frecuzrdgg 10157 frecuzrdgsuctlem 10164 seqeq2 10190 seqeq3 10191 iseqvalcbv 10198 seq3val 10199 seqvalcd 10200 eucalgval 11662 ennnfonelemp1 11846 ennnfonelemnn0 11862 strsetsid 11919 ressid2 11945 ressval2 11946 |
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