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	$$⊢A\times \varnothing =\varnothing$$

Proof

Step	Hyp	Ref	Expression
1		0xp	$$⊢\varnothing \times A=\varnothing$$
2	1	cnveqi	$$⊢{\left(\varnothing \times A\right)}^{-1}={\varnothing }^{-1}$$
3		cnvxp	$$⊢{\left(\varnothing \times A\right)}^{-1}=A\times \varnothing$$
4		cnv0	$$⊢{\varnothing }^{-1}=\varnothing$$
5	2 3 4	3eqtr3i	$$⊢A\times \varnothing =\varnothing$$