Theorem sbf 1826

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 1568	. 2 |- ( ph -> A. x ph )
3	2	sbh 1825	1 |- ( [ y / x ] ph <-> ph )

Syntax hints:   <-> wb 105   F/wnf 1509   [wsb 1811

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-i9 1579  ax-ial 1583

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812

This theorem is referenced by:  sbf2  1827  sbequ5  1831  sbequ6  1832  sbt  1833  sblim  2013  moimv  2149  moanim  2157  sbabel  2413  nfcdeq  3041  oprcl  3909