Theorem ixpconst

Description: Infinite Cartesian product of a constant B . (Contributed by NM, 28-Sep-2006)

	Ref	Expression
Hypotheses	ixpconst.1	⊢ 𝐴 ∈ V
	ixpconst.2	⊢ 𝐵 ∈ V
Assertion	ixpconst	⊢ X 𝑥 ∈ 𝐴 𝐵 = ( 𝐵 ↑m 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		ixpconst.1	⊢ 𝐴 ∈ V
2		ixpconst.2	⊢ 𝐵 ∈ V
3		ixpconstg	⊢ ( ( 𝐴 ∈ V ∧ 𝐵 ∈ V ) → X 𝑥 ∈ 𝐴 𝐵 = ( 𝐵 ↑m 𝐴 ) )
4	1 2 3	mp2an	⊢ X 𝑥 ∈ 𝐴 𝐵 = ( 𝐵 ↑m 𝐴 )