Theorem xp0OLD

Description: Obsolete version of xp0 as of 1-Feb-2026. (Contributed by NM, 12-Apr-2004) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	xp0OLD	⊢ ( 𝐴 × ∅ ) = ∅

Proof

Step	Hyp	Ref	Expression
1		0xp	⊢ ( ∅ × 𝐴 ) = ∅
2	1	cnveqi	⊢ ◡ ( ∅ × 𝐴 ) = ◡ ∅
3		cnvxp	⊢ ◡ ( ∅ × 𝐴 ) = ( 𝐴 × ∅ )
4		cnv0	⊢ ◡ ∅ = ∅
5	2 3 4	3eqtr3i	⊢ ( 𝐴 × ∅ ) = ∅