Theorem bj-sbfv 32764

Description: Version of sbf 2380 with a dv condition, which does not require ax-13 2246. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-sbfv.1	|- F/ x ph

Assertion

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

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y)

Proof of Theorem bj-sbfv

Step	Hyp	Ref	Expression
1		bj-sbfv.1	. 2 |- F/ x ph
2		bj-sbftv 32763	. 2 |- ( F/ x ph -> ( [ y / x ] ph <-> ph ) )
3	1, 2	ax-mp 5	1 |- ( [ y / x ] ph <-> ph )

Syntax hints:   <-> wb 196   F/wnf 1708   [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-12 2047

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)