Theorem bnj931

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypothesis	bnj931.1	⊢ 𝐴 = ( 𝐵 ∪ 𝐶 )
Assertion	bnj931	⊢ 𝐵 ⊆ 𝐴

Proof

Step	Hyp	Ref	Expression
1		bnj931.1	⊢ 𝐴 = ( 𝐵 ∪ 𝐶 )
2		ssun1	⊢ 𝐵 ⊆ ( 𝐵 ∪ 𝐶 )
3	2 1	sseqtrri	⊢ 𝐵 ⊆ 𝐴