Theorem bnj1424

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

	Ref	Expression
Hypothesis	bnj1424.1	$$⊢A=B\cup C$$
Assertion	bnj1424	$$⊢D\in A\to \left(D\in B\vee D\in C\right)$$

Proof

Step	Hyp	Ref	Expression
1		bnj1424.1	$$⊢A=B\cup C$$
2	1	bnj1138	$$⊢D\in A\leftrightarrow \left(D\in B\vee D\in C\right)$$
3	2	biimpi	$$⊢D\in A\to \left(D\in B\vee D\in C\right)$$