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

Theorem dvelimnf 1957
Description: Version of dvelim 1956 using "not free" notation. (Contributed by Mario Carneiro, 9-Oct-2016.)
Hypotheses
Ref Expression
dvelimnf.1  |-  F/ x ph
dvelimnf.2  |-  ( z  =  y  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
dvelimnf  |-  ( -. 
A. x  x  =  y  ->  F/ x ps )
Distinct variable group:    ps, z
Allowed substitution hints:    ph( x, y, z)    ps( x, y)

Proof of Theorem dvelimnf
StepHypRef Expression
1 dvelimnf.1 . 2  |-  F/ x ph
2 nfv 1605 . 2  |-  F/ z ps
3 dvelimnf.2 . 2  |-  ( z  =  y  ->  ( ph 
<->  ps ) )
41, 2, 3dvelimf 1937 1  |-  ( -. 
A. x  x  =  y  ->  F/ x ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176   A.wal 1527   F/wnf 1531
This theorem is referenced by:  nfrab  2721
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532
  Copyright terms: Public domain W3C validator