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Theorem op1stb 4750
 Description: Extract the first member of an ordered pair. Theorem 73 of [Suppes] p. 42. (See op2ndb 5345 to extract the second member, op1sta 5343 for an alternate version, and op1st 6347 for the preferred version.) (Contributed by NM, 25-Nov-2003.)
Hypotheses
Ref Expression
op1stb.1
op1stb.2
Assertion
Ref Expression
op1stb

Proof of Theorem op1stb
StepHypRef Expression
1 op1stb.1 . . . . . 6
2 op1stb.2 . . . . . 6
31, 2dfop 3975 . . . . 5
43inteqi 4046 . . . 4
5 snex 4397 . . . . . 6
6 prex 4398 . . . . . 6
75, 6intpr 4075 . . . . 5
8 snsspr1 3939 . . . . . 6
9 df-ss 3326 . . . . . 6
108, 9mpbi 200 . . . . 5
117, 10eqtri 2455 . . . 4
124, 11eqtri 2455 . . 3
1312inteqi 4046 . 2
141intsn 4078 . 2
1513, 14eqtri 2455 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   wcel 1725  cvv 2948   cin 3311   wss 3312  csn 3806  cpr 3807  cop 3809  cint 4042 This theorem is referenced by:  elreldm  5086  op2ndb  5345  elxp5  5350  1stval2  6356  fundmen  7172  xpsnen  7184  xpnnenOLD  12799 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-int 4043
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