Theorem sbf 1700

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 1452	. 2 |- ( ph -> A. x ph )
3	2	sbh 1699	1 |- ( [ y / x ] ph <-> ph )

Syntax hints:   <-> wb 103   F/wnf 1389   [wsb 1685

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-4 1440  ax-i9 1463  ax-ial 1467

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-sb 1686

This theorem is referenced by:  sbf2  1701  sbequ5  1705  sbequ6  1706  sbt  1707  sblim  1872  moimv  2007  moanim  2015  sbabel  2244  nfcdeq  2812  oprcl  3594