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Mirrors > Home > ILE Home > Th. List > op2ndb | Unicode version |
Description: Extract the second member of an ordered pair. Theorem 5.12(ii) of [Monk1] p. 52. (See op1stb 4450 to extract the first member and op2nda 5082 for an alternate version.) (Contributed by NM, 25-Nov-2003.) |
Ref | Expression |
---|---|
cnvsn.1 | |
cnvsn.2 |
Ref | Expression |
---|---|
op2ndb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvsn.1 | . . . . . . 7 | |
2 | cnvsn.2 | . . . . . . 7 | |
3 | 1, 2 | cnvsn 5080 | . . . . . 6 |
4 | 3 | inteqi 3822 | . . . . 5 |
5 | 2, 1 | opex 4201 | . . . . . 6 |
6 | 5 | intsn 3853 | . . . . 5 |
7 | 4, 6 | eqtri 2185 | . . . 4 |
8 | 7 | inteqi 3822 | . . 3 |
9 | 8 | inteqi 3822 | . 2 |
10 | 2, 1 | op1stb 4450 | . 2 |
11 | 9, 10 | eqtri 2185 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1342 wcel 2135 cvv 2721 csn 3570 cop 3573 cint 3818 ccnv 4597 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-int 3819 df-br 3977 df-opab 4038 df-xp 4604 df-rel 4605 df-cnv 4606 |
This theorem is referenced by: 2ndval2 6116 |
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