Theorem just2-df

Description: Second justification theorem for definitions whose definiens is a conjunction, as in df-sb . If ph is equivalent to ( ps /\ ch ) , then it implies ( ps <-> ch ) . In the case of df-sb , this expresses the invariance of the definition under alpha-renaming of the bound variable. (Contributed by Wolf Lammen, 6-Jun-2026)

	Ref	Expression
Hypothesis	just2-df.1	|- ( ph <-> ( ps /\ ch ) )
Assertion	just2-df	|- ( ph -> ( ps <-> ch ) )

Proof

Step	Hyp	Ref	Expression
1		just2-df.1	|- ( ph <-> ( ps /\ ch ) )
2		abab	|- ( ( ps /\ ch ) <-> ( ps /\ ( ps <-> ch ) ) )
3	1 2	bitri	|- ( ph <-> ( ps /\ ( ps <-> ch ) ) )
4	3	simprbi	|- ( ph -> ( ps <-> ch ) )