MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfna1 Structured version   Unicode version

Theorem nfna1 1839
Description: A convenience theorem particularly designed to remove dependencies on ax-11 1782 in conjunction with disjunctors. (Contributed by Wolf Lammen, 2-Sep-2018.)
Assertion
Ref Expression
nfna1  |-  F/ x  -.  A. x ph

Proof of Theorem nfna1
StepHypRef Expression
1 nfa1 1833 . 2  |-  F/ x A. x ph
21nfn 1837 1  |-  F/ x  -.  A. x ph
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   A.wal 1368   F/wnf 1590
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-12 1794
This theorem depends on definitions:  df-bi 185  df-ex 1588  df-nf 1591
This theorem is referenced by:  dvelimhw  1890  nfeqf  2002  equs5  2049  nfsb2  2057  sbco2  2118  sbco3  2121  sb9  2133  axpowndlem2  8863  axpowndlem3  8865  axregnd  8871  wl-cbvalnaed  28499  wl-equsb3  28518  wl-sbcom2d-lem1  28523  wl-mo2dnae  28533  wl-ax11-lem3  28541  wl-ax11-lem4  28542  wl-ax11-lem6  28544  wl-ax11-lem7  28545  bj-equs5v  32567  bj-nfsb2v  32575
  Copyright terms: Public domain W3C validator