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Theorem nfpr 3773
 Description: Bound-variable hypothesis builder for unordered pairs. (Contributed by NM, 14-Nov-1995.)
Hypotheses
Ref Expression
nfpr.1 xA
nfpr.2 xB
Assertion
Ref Expression
nfpr x{A, B}

Proof of Theorem nfpr
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 dfpr2 3749 . 2 {A, B} = {y (y = A y = B)}
2 nfpr.1 . . . . 5 xA
32nfeq2 2500 . . . 4 x y = A
4 nfpr.2 . . . . 5 xB
54nfeq2 2500 . . . 4 x y = B
63, 5nfor 1836 . . 3 x(y = A y = B)
76nfab 2493 . 2 x{y (y = A y = B)}
81, 7nfcxfr 2486 1 x{A, B}
 Colors of variables: wff setvar class Syntax hints:   ∨ wo 357   = wceq 1642  {cab 2339  Ⅎwnfc 2476  {cpr 3738 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 This theorem is referenced by:  nfsn  3784  nfopk  4068
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