Theorem nanbi2d 1462

Description: Introduce a left anti-conjunct to both sides of a logical equivalence. (Contributed by SF, 2-Jan-2018.)

Hypothesis

Ref	Expression
nanbid.1	|- ( ph -> ( ps <-> ch ) )

Assertion

Ref	Expression
nanbi2d	|- ( ph -> ( ( th -/\ ps ) <-> ( th -/\ ch ) ) )

Proof of Theorem nanbi2d

Step	Hyp	Ref	Expression
1		nanbid.1	. 2 |- ( ph -> ( ps <-> ch ) )
2		nanbi2 1456	. 2 |- ( ( ps <-> ch ) -> ( ( th -/\ ps ) <-> ( th -/\ ch ) ) )
3	1, 2	syl 17	1 |- ( ph -> ( ( th -/\ ps ) <-> ( th -/\ ch ) ) )

Syntax hints:   -> wi 4   <-> wb 196   -/\ wnan 1447

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-nan 1448

This theorem is referenced by: (None)