New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  nfres GIF version

Theorem nfres 4936
 Description: Bound-variable hypothesis builder for restriction. (Contributed by NM, 15-Sep-2003.) (Revised by David Abernethy, 19-Jun-2012.)
Hypotheses
Ref Expression
nfres.1 xA
nfres.2 xB
Assertion
Ref Expression
nfres x(A B)

Proof of Theorem nfres
StepHypRef Expression
1 df-res 4788 . 2 (A B) = (A ∩ (B × V))
2 nfres.1 . . 3 xA
3 nfres.2 . . . 4 xB
4 nfcv 2489 . . . 4 xV
53, 4nfxp 4810 . . 3 x(B × V)
62, 5nfin 3230 . 2 x(A ∩ (B × V))
71, 6nfcxfr 2486 1 x(A B)
 Colors of variables: wff setvar class Syntax hints:  Ⅎwnfc 2476  Vcvv 2859   ∩ cin 3208   × cxp 4770   ↾ cres 4774 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-nin 3211  df-compl 3212  df-in 3213  df-opab 4623  df-xp 4784  df-res 4788 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator