Theorem nfs1f 1791

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 1530	. . 3 |- ( ph -> A. x ph )
3	2	sbh 1787	. 2 |- ( [ y / x ] ph <-> ph )
4	3, 1	nfxfr 1485	1 |- F/ x [ y / x ] ph

Syntax hints:   F/wnf 1471   [wsb 1773

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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-i9 1541  ax-ial 1545

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774

This theorem is referenced by: (None)