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Theorem op1stb 4460
 Description: Extract the first member of an ordered pair. Theorem 73 of [Suppes] p. 42. (See op2ndb 5062 to extract the second member, op1sta 5060 for an alternate version, and op1st 5980 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 3695 . . . . 5
43inteqi 3764 . . . 4
5 snex 4110 . . . . . 6
6 prex 4111 . . . . . 6
75, 6intpr 3793 . . . . 5
8 snsspr1 3664 . . . . . 6
9 df-ss 3089 . . . . . 6
108, 9mpbi 201 . . . . 5
117, 10eqtri 2273 . . . 4
124, 11eqtri 2273 . . 3
1312inteqi 3764 . 2
141intsn 3796 . 2
1513, 14eqtri 2273 1
 Colors of variables: wff set class Syntax hints:   wceq 1619   wcel 1621  cvv 2727   cin 3077   wss 3078  csn 3544  cpr 3545  cop 3547  cint 3760 This theorem is referenced by:  elreldm  4810  op2ndb  5062  elxp5  5067  1stval2  5989  fundmen  6819  xpsnen  6831  xpnnenOLD  12362 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 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pr 4108 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 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-ral 2513  df-v 2729  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553  df-int 3761
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