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Metamath Proof Explorer

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 ∈ A B = B A

Proof

Step Hyp Ref Expression
1 ixpconst.1 ⊢ A ∈ V
2 ixpconst.2 ⊢ B ∈ V
3 ixpconstg ⊢ A ∈ V ∧ B ∈ V → ⨉ x ∈ A B = B A
4 1 2 3 mp2an ⊢ ⨉ x ∈ A B = B A