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Theorem dvelimnf 2022
Description: Version of dvelim 2019 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 1626 . 2  |-  F/ z ps
3 dvelimnf.2 . 2  |-  ( z  =  y  ->  ( ph 
<->  ps ) )
41, 2, 3dvelimf 2021 1  |-  ( -. 
A. x  x  =  y  ->  F/ x ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 177   A.wal 1546   F/wnf 1550
This theorem is referenced by:  nfrab  2857
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551
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