Theorem sbh 2381

Description: Substitution for a variable not free in a wff does not affect it. (Contributed by NM, 14-May-1993.)

Hypothesis

Ref	Expression
sbh.1	|- ( ph -> A. x ph )

Assertion

Ref	Expression
sbh	|- ( [ y / x ] ph <-> ph )

Proof of Theorem sbh

Step	Hyp	Ref	Expression
1		sbh.1	. . 3 |- ( ph -> A. x ph )
2	1	nf5i 2024	. 2 |- F/ x ph
3	2	sbf 2380	1 |- ( [ y / x ] ph <-> ph )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-nf 1710  df-sb 1881

This theorem is referenced by: (None)