Theorem nanbi1d 1461

Description: Introduce a right 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
nanbi1d	|- ( ph -> ( ( ps -/\ th ) <-> ( ch -/\ th ) ) )

Proof of Theorem nanbi1d

Step	Hyp	Ref	Expression
1		nanbid.1	. 2 |- ( ph -> ( ps <-> ch ) )
2		nanbi1 1455	. 2 |- ( ( ps <-> ch ) -> ( ( ps -/\ th ) <-> ( ch -/\ th ) ) )
3	1, 2	syl 17	1 |- ( ph -> ( ( ps -/\ th ) <-> ( ch -/\ th ) ) )

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)