Theorem sbf 1787

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 1529	. 2 |- ( ph -> A. x ph )
3	2	sbh 1786	1 |- ( [ y / x ] ph <-> ph )

Syntax hints:   <-> wb 105   F/wnf 1470   [wsb 1772

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 1457  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-4 1520  ax-i9 1540  ax-ial 1544

This theorem depends on definitions:  df-bi 117  df-nf 1471  df-sb 1773

This theorem is referenced by:  sbf2  1788  sbequ5  1792  sbequ6  1793  sbt  1794  sblim  1967  moimv  2102  moanim  2110  sbabel  2356  nfcdeq  2971  oprcl  3814