Theorem bj-sbtv 32766

Description: Version of sbt 2419 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-sbtv.1	|- ph

Assertion

Ref	Expression
bj-sbtv	|- [ y / x ] ph

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y)

Proof of Theorem bj-sbtv

Step	Hyp	Ref	Expression
1		bj-stdpc4v 32754	. 2 |- ( A. x ph -> [ y / x ] ph )
2		bj-sbtv.1	. 2 |- ph
3	1, 2	mpg 1724	1 |- [ y / x ] ph

Syntax hints:   [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-sb 1881

This theorem is referenced by:  bj-vjust  32786