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Theorem dvelimnf 2076
Description: Version of dvelim 2074 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 1630 . 2  |-  F/ z ps
3 dvelimnf.2 . 2  |-  ( z  =  y  ->  ( ph 
<->  ps ) )
41, 2, 3dvelimf 2069 1  |-  ( -. 
A. x  x  =  y  ->  F/ x ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 178   A.wal 1550   F/wnf 1554
This theorem is referenced by:  nfrab  2891
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555
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