Theorem simplbiim

Description: Implication from an eliminated conjunct equivalent to the antecedent. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Proof shortened by Wolf Lammen, 26-Mar-2022)

	Ref	Expression
Hypotheses	simplbiim.1	|- ( ph <-> ( ps /\ ch ) )
	simplbiim.2	|- ( ch -> th )
Assertion	simplbiim	|- ( ph -> th )

Proof

Step	Hyp	Ref	Expression
1		simplbiim.1	|- ( ph <-> ( ps /\ ch ) )
2		simplbiim.2	|- ( ch -> th )
3	1	simprbi	|- ( ph -> ch )
4	3 2	syl	|- ( ph -> th )