Theorem nanbi1d

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

	Ref	Expression
Hypothesis	nanbid.1	|- ( ph -> ( ps <-> ch ) )
Assertion	nanbi1d	|- ( ph -> ( ( ps -/\ th ) <-> ( ch -/\ th ) ) )

Proof

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