Theorem sbf 1714

Description: Substitution for a variable not free in a wff does not affect it. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 4-Oct-2016.)

Hypothesis

Ref	Expression
sbf.1	|- F/ x ph

Assertion

Ref	Expression
sbf	|- ( [ y / x ] ph <-> ph )

Proof of Theorem sbf

Step	Hyp	Ref	Expression
1		sbf.1	. . 3 |- F/ x ph
2	1	nfri 1464	. 2 |- ( ph -> A. x ph )
3	2	sbh 1713	1 |- ( [ y / x ] ph <-> ph )

Syntax hints:   <-> wb 104   F/wnf 1401   [wsb 1699

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 1388  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-4 1452  ax-i9 1475  ax-ial 1479

This theorem depends on definitions:  df-bi 116  df-nf 1402  df-sb 1700

This theorem is referenced by:  sbf2  1715  sbequ5  1719  sbequ6  1720  sbt  1721  sblim  1886  moimv  2021  moanim  2029  sbabel  2261  nfcdeq  2851  oprcl  3668