Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfifd Unicode version

Theorem nfifd 3969
 Description: Deduction version of nfif 3970. (Contributed by NM, 15-Feb-2013.) (Revised by Mario Carneiro, 13-Oct-2016.)
Hypotheses
Ref Expression
nfifd.2
nfifd.3
nfifd.4
Assertion
Ref Expression
nfifd

Proof of Theorem nfifd
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfif2 3943 . 2
2 nfv 1707 . . 3
3 nfifd.4 . . . . . 6
43nfcrd 2625 . . . . 5
5 nfifd.2 . . . . 5
64, 5nfimd 1917 . . . 4
7 nfifd.3 . . . . . 6
87nfcrd 2625 . . . . 5
98, 5nfand 1925 . . . 4
106, 9nfimd 1917 . . 3
112, 10nfabd 2641 . 2
121, 11nfcxfrd 2618 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  F/wnf 1616  e.wcel 1818  {cab 2442  F/_wnfc 2605  ifcif 3941 This theorem is referenced by:  nfif  3970 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-if 3942
 Copyright terms: Public domain W3C validator