Theorem sbf 1800

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 1542	. 2 |- ( ph -> A. x ph )
3	2	sbh 1799	1 |- ( [ y / x ] ph <-> ph )

Syntax hints:   <-> wb 105   F/wnf 1483   [wsb 1785

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 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-4 1533  ax-i9 1553  ax-ial 1557

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786

This theorem is referenced by:  sbf2  1801  sbequ5  1805  sbequ6  1806  sbt  1807  sblim  1985  moimv  2120  moanim  2128  sbabel  2375  nfcdeq  2995  oprcl  3843