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Theorem prid1 3467
Description: An unordered pair contains its first member. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
prid1.1 A V
Assertion
Ref Expression
prid1 A {A, B}

Proof of Theorem prid1
StepHypRef Expression
1 prid1.1 . 2 A V
2 prid1g 3465 . 2 (A V → A {A, B})
31, 2ax-mp 7 1 A {A, B}
Colors of variables: wff set class
Syntax hints:   wcel 1390  Vcvv 2551  {cpr 3368
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374
This theorem is referenced by:  prid2  3468  prnz  3481  preqr1  3530  preq12b  3532  prel12  3533  opi1  3960  opeluu  4148  onsucelsucexmidlem1  4213  regexmidlem1  4218  opthreg  4234  dmrnssfld  4538  funopg  4877  acexmidlemb  5447  2dom  6221  reelprrecn  6794  pnfxr  8442  bdop  9310
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