Theorem wrddun2

Description: Superadditivity of word constructor. Class of words over union alphabet includes all words over either alphabet in the union; if B and C are non-empty and different, then this subclass relation is strict because of the words which have symbols both from B and from C . (Contributed by Ender Ting, 24-Jul-2026)

	Ref	Expression
Assertion	wrddun2	|- ( Word B u. Word C ) C_ Word ( B u. C )

Proof

Step	Hyp	Ref	Expression
1		elun	|- ( n e. ( Word B u. Word C ) <-> ( n e. Word B \/ n e. Word C ) )
2		wrddun	|- ( ( n e. Word B \/ n e. Word C ) -> n e. Word ( B u. C ) )
3	1 2	sylbi	|- ( n e. ( Word B u. Word C ) -> n e. Word ( B u. C ) )
4	3	ssriv	|- ( Word B u. Word C ) C_ Word ( B u. C )