Theorem nfs1f 1734

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 1480	. . 3 |- ( ph -> A. x ph )
3	2	sbh 1730	. 2 |- ( [ y / x ] ph <-> ph )
4	3, 1	nfxfr 1431	1 |- F/ x [ y / x ] ph

Syntax hints:   F/wnf 1417   [wsb 1716

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1404  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-4 1468  ax-i9 1491  ax-ial 1495

This theorem depends on definitions:  df-bi 116  df-nf 1418  df-sb 1717

This theorem is referenced by: (None)