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Theorem op2ndb 5031
 Description: Extract the second member of an ordered pair. Theorem 5.12(ii) of [Monk1] p. 52. (See op1stb 4408 to extract the first member and op2nda 5032 for an alternate version.) (Contributed by NM, 25-Nov-2003.)
Hypotheses
Ref Expression
cnvsn.1
cnvsn.2
Assertion
Ref Expression
op2ndb

Proof of Theorem op2ndb
StepHypRef Expression
1 cnvsn.1 . . . . . . 7
2 cnvsn.2 . . . . . . 7
31, 2cnvsn 5030 . . . . . 6
43inteqi 3784 . . . . 5
52, 1opex 4160 . . . . . 6
65intsn 3815 . . . . 5
74, 6eqtri 2161 . . . 4
87inteqi 3784 . . 3
98inteqi 3784 . 2
102, 1op1stb 4408 . 2
119, 10eqtri 2161 1
 Colors of variables: wff set class Syntax hints:   wceq 1332   wcel 1481  cvv 2690  csn 3533  cop 3536  cint 3780  ccnv 4547 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-14 1493  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4055  ax-pow 4107  ax-pr 4140 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2692  df-un 3081  df-in 3083  df-ss 3090  df-pw 3518  df-sn 3539  df-pr 3540  df-op 3542  df-int 3781  df-br 3939  df-opab 3999  df-xp 4554  df-rel 4555  df-cnv 4556 This theorem is referenced by:  2ndval2  6063
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