Theorem bj-ssbbii 32624

Description: Biconditional property for substitution. Uses only ax-1--5. (Contributed by BJ, 22-Dec-2020.)

Hypothesis

Ref	Expression
bj-ssbbii.1	|- ( ph <-> ps )

Assertion

Ref	Expression
bj-ssbbii	|- ([ t/ x]b ph <-> [ t/ x]b ps )

Proof of Theorem bj-ssbbii

Step	Hyp	Ref	Expression
1		bj-ssbbi 32622	. 2 |- ( A. x ( ph <-> ps ) -> ([ t/ x]b ph <-> [ t/ x]b ps ) )
2		bj-ssbbii.1	. 2 |- ( ph <-> ps )
3	1, 2	mpg 1724	1 |- ([ t/ x]b ph <-> [ t/ x]b ps )

Syntax hints:   <-> wb 196  [wssb 32619

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

This theorem depends on definitions:  df-bi 197  df-ssb 32620

This theorem is referenced by:  bj-ssbssblem  32649  bj-ssbcom3lem  32650