Theorem just1-df

Description: First justification theorem for definitions whose definiens is a conjunction, as in df-sb . Here ph denotes the definiendum, while ps and ch represent the two components of the definiens. The theorem shows that the definiendum implies either component separately. (Contributed by Wolf Lammen, 6-Jun-2026) (New usage is discouraged.)

	Ref	Expression
Hypothesis	just1-df.1	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) )
Assertion	just1-df	⊢ ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		just1-df.1	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) )
2	1	simplbi	⊢ ( 𝜑 → 𝜓 )