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Theorem nfopk 4068
 Description: Bound-variable hypothesis builder for ordered pairs. (Contributed by NM, 14-Nov-1995.)
Hypotheses
Ref Expression
nfopk.1 xA
nfopk.2 xB
Assertion
Ref Expression
nfopk xA, B

Proof of Theorem nfopk
StepHypRef Expression
1 df-opk 4058 . 2 A, B⟫ = {{A}, {A, B}}
2 nfopk.1 . . . 4 xA
32nfsn 3784 . . 3 x{A}
4 nfopk.2 . . . 4 xB
52, 4nfpr 3773 . . 3 x{A, B}
63, 5nfpr 3773 . 2 x{{A}, {A, B}}
71, 6nfcxfr 2486 1 xA, B
 Colors of variables: wff setvar class Syntax hints:  Ⅎwnfc 2476  {csn 3737  {cpr 3738  ⟪copk 4057 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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  df-opk 4058 This theorem is referenced by: (None)
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