MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfsb2 Unicode version

Theorem nfsb2 1998
Description: Bound-variable hypothesis builder for substitution. (Contributed by Mario Carneiro, 4-Oct-2016.)
Assertion
Ref Expression
nfsb2  |-  ( -. 
A. x  x  =  y  ->  F/ x [ y  /  x ] ph )

Proof of Theorem nfsb2
StepHypRef Expression
1 nfnae 1896 . 2  |-  F/ x  -.  A. x  x  =  y
2 hbsb2 1997 . 2  |-  ( -. 
A. x  x  =  y  ->  ( [
y  /  x ] ph  ->  A. x [ y  /  x ] ph ) )
31, 2nfd 1746 1  |-  ( -. 
A. x  x  =  y  ->  F/ x [ 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:  sbequi  1999  nfsb4t  2020  sbco3  2028
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
  Copyright terms: Public domain W3C validator