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Theorem nfsb4 2021
Description: A variable not free remains so after substitution with a distinct variable. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 4-Oct-2016.)
Hypothesis
Ref Expression
nfsb4.1  |-  F/ z
ph
Assertion
Ref Expression
nfsb4  |-  ( -. 
A. z  z  =  y  ->  F/ z [ y  /  x ] ph )

Proof of Theorem nfsb4
StepHypRef Expression
1 nfsb4t 2020 . 2  |-  ( A. x F/ z ph  ->  ( -.  A. z  z  =  y  ->  F/ z [ y  /  x ] ph ) )
2 nfsb4.1 . 2  |-  F/ z
ph
31, 2mpg 1535 1  |-  ( -. 
A. z  z  =  y  ->  F/ z [ y  /  x ] ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527   F/wnf 1531   [wsb 1629
This theorem is referenced by:  sbco2  2026  nfsb  2048  sbal1  2065
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  df-sb 1630
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