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 u. C )
Assertion	bnj1424	|- ( D e. A -> ( D e. B \/ D e. C ) )

Proof

Step	Hyp	Ref	Expression
1		bnj1424.1	|- A = ( B u. C )
2	1	bnj1138	|- ( D e. A <-> ( D e. B \/ D e. C ) )
3	2	biimpi	|- ( D e. A -> ( D e. B \/ D e. C ) )