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Theorem nfsb4 2129
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 2127 . 2  |-  ( A. x F/ z ph  ->  ( -.  A. z  z  =  y  ->  F/ z [ y  /  x ] ph ) )
2 nfsb4.1 . 2  |-  F/ z
ph
31, 2mpg 1557 1  |-  ( -. 
A. z  z  =  y  ->  F/ z [ y  /  x ] ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1549   F/wnf 1553   [wsb 1658
This theorem is referenced by:  sbco2  2161  nfsb  2185  sbal1  2203
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659
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