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Theorem op2ndb 5143
 Description: Extract the second member of an ordered pair. Theorem 5.12(ii) of [Monk1] p. 52. (See op1stb 4541 to extract the first member, op2nda 5144 for an alternate version, and op2nd 6063 for the preferred 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 5142 . . . . . 6
43inteqi 3840 . . . . 5
5 opex 4209 . . . . . 6
65intsn 3872 . . . . 5
74, 6eqtri 2278 . . . 4
87inteqi 3840 . . 3
98inteqi 3840 . 2
102, 1op1stb 4541 . 2
119, 10eqtri 2278 1
 Colors of variables: wff set class Syntax hints:   wceq 1619   wcel 1621  cvv 2763  csn 3614  cop 3617  cint 3836  ccnv 4660 This theorem is referenced by:  2ndval2  6072 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2239  ax-sep 4115  ax-nul 4123  ax-pr 4186 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-eu 2122  df-mo 2123  df-clab 2245  df-cleq 2251  df-clel 2254  df-nfc 2383  df-ne 2423  df-ral 2523  df-rex 2524  df-rab 2527  df-v 2765  df-dif 3130  df-un 3132  df-in 3134  df-ss 3141  df-nul 3431  df-if 3540  df-sn 3620  df-pr 3621  df-op 3623  df-int 3837  df-br 3998  df-opab 4052  df-xp 4675  df-rel 4676  df-cnv 4677
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