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Theorem prid1g 3825
 Description: An unordered pair contains its first member. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by Stefan Allan, 8-Nov-2008.)
Assertion
Ref Expression
prid1g (A VA {A, B})

Proof of Theorem prid1g
StepHypRef Expression
1 eqid 2353 . . 3 A = A
21orci 379 . 2 (A = A A = B)
3 elprg 3750 . 2 (A V → (A {A, B} ↔ (A = A A = B)))
42, 3mpbiri 224 1 (A VA {A, B})
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∨ wo 357   = wceq 1642   ∈ wcel 1710  {cpr 3738 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-sn 3741  df-pr 3742 This theorem is referenced by:  prid2g  3826  prid1  3827  opkth1g  4130
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