Theorem bnj1149

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

	Ref	Expression
Hypotheses	bnj1149.1	|- ( ph -> A e. _V )
	bnj1149.2	|- ( ph -> B e. _V )
Assertion	bnj1149	|- ( ph -> ( A u. B ) e. _V )

Proof

Step	Hyp	Ref	Expression
1		bnj1149.1	|- ( ph -> A e. _V )
2		bnj1149.2	|- ( ph -> B e. _V )
3		unexg	|- ( ( A e. _V /\ B e. _V ) -> ( A u. B ) e. _V )
4	1 2 3	syl2anc	|- ( ph -> ( A u. B ) e. _V )