Theorem nfs1f 1802

Description: If x is not free in ph, it is not free in [ y / x ] ph. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
nfs1f.1	|- F/ x ph

Assertion

Ref	Expression
nfs1f	|- F/ x [ y / x ] ph

Proof of Theorem nfs1f

Step	Hyp	Ref	Expression
1		nfs1f.1	. . . 4 |- F/ x ph
2	1	nfri 1541	. . 3 |- ( ph -> A. x ph )
3	2	sbh 1798	. 2 |- ( [ y / x ] ph <-> ph )
4	3, 1	nfxfr 1496	1 |- F/ x [ y / x ] ph

Syntax hints:   F/wnf 1482   [wsb 1784

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1469  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-4 1532  ax-i9 1552  ax-ial 1556

This theorem depends on definitions:  df-bi 117  df-nf 1483  df-sb 1785

This theorem is referenced by: (None)