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

Theorem nfif 3686
 Description: Bound-variable hypothesis builder for a conditional operator. (Contributed by NM, 16-Feb-2005.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Hypotheses
Ref Expression
nfif.1
nfif.2
nfif.3
Assertion
Ref Expression
nfif

Proof of Theorem nfif
StepHypRef Expression
1 nfif.1 . . . 4
21a1i 10 . . 3
3 nfif.2 . . . 4
43a1i 10 . . 3
5 nfif.3 . . . 4
65a1i 10 . . 3
72, 4, 6nfifd 3685 . 2
87trud 1323 1
 Colors of variables: wff setvar class Syntax hints:   wtru 1316  wnf 1544  wnfc 2476  cif 3662 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-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-if 3663 This theorem is referenced by:  csbifg  3690
 Copyright terms: Public domain W3C validator