Theorem nfsbv 1920

Description: If z is not free in ph, it is not free in [ y / x ] ph when z is distinct from x and y. Version of nfsb 1919 requiring more disjoint variables. (Contributed by Wolf Lammen, 7-Feb-2023.) Remove disjoint variable condition on x , y. (Revised by Steven Nguyen, 13-Aug-2023.)

Hypothesis

Ref	Expression
nfsbv.nf	|- F/ z ph

Assertion

Ref	Expression
nfsbv	|- F/ z [ y / x ] ph

Distinct variable groups:   x, z   y, z

Allowed substitution hints:   ph( x, y, z)

Proof of Theorem nfsbv

Step	Hyp	Ref	Expression
1		nfsbv.nf	. 2 |- F/ z ph
2	1	nfsb 1919	1 |- F/ z [ y / x ] ph

Syntax hints:   F/wnf 1436   [wsb 1735

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736

This theorem is referenced by:  sbco2v  1921