Theorem sbf 1823

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 1565	. 2 |- ( ph -> A. x ph )
3	2	sbh 1822	1 |- ( [ y / x ] ph <-> ph )

Syntax hints:   <-> wb 105   F/wnf 1506   [wsb 1808

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-i9 1576  ax-ial 1580

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809

This theorem is referenced by:  sbf2  1824  sbequ5  1828  sbequ6  1829  sbt  1830  sblim  2008  moimv  2144  moanim  2152  sbabel  2399  nfcdeq  3025  oprcl  3881