Theorem ndmov

Description: The value of an operation outside its domain. (Contributed by NM, 24-Aug-1995)

	Ref	Expression
Hypothesis	ndmov.1	$$⊢\mathrm{dom}F=S\times S$$
Assertion	ndmov	$$⊢\neg \left(A\in S\wedge B\in S\right)\to AFB=\varnothing$$

Proof

Step	Hyp	Ref	Expression
1		ndmov.1	$$⊢\mathrm{dom}F=S\times S$$
2		ndmovg	$$⊢\left(\mathrm{dom}F=S\times S\wedge \neg \left(A\in S\wedge B\in S\right)\right)\to AFB=\varnothing$$
3	1 2	mpan	$$⊢\neg \left(A\in S\wedge B\in S\right)\to AFB=\varnothing$$