Theorem bj-axbun

Description: Two ways of stating the axiom of binary union (which is the universal closure of either side, see ax-bj-bun ). (Contributed by BJ, 12-Jan-2025) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-axbun	|- ( ( x u. y ) e. _V <-> E. z A. t ( t e. z <-> ( t e. x \/ t e. y ) ) )

Proof

Step	Hyp	Ref	Expression
1		elun	|- ( t e. ( x u. y ) <-> ( t e. x \/ t e. y ) )
2	1	bj-clex	|- ( ( x u. y ) e. _V <-> E. z A. t ( t e. z <-> ( t e. x \/ t e. y ) ) )