Definition df-goor

Description: Define the Godel-set of disjunction. Here the arguments U and V are also Godel-sets corresponding to smaller formulas. Note that this is aclass expression, not a wff. (Contributed by Mario Carneiro, 14-Jul-2013)

	Ref	Expression
Assertion	df-goor	$$⊢{\vee }_{𝑔}=\left(u\in \mathrm{V},v\in \mathrm{V}⟼\left[{\neg }_{𝑔}u\right]{\to }_{𝑔}v\right)$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cgoo	$$class{\vee }_{𝑔}$$
1		vu	$$setvaru$$
2		cvv	$$class\mathrm{V}$$
3		vv	$$setvarv$$
4	1	cv	$$setvaru$$
5	4	cgon	$$class\left[{\neg }_{𝑔}u\right]$$
6		cgoi	$$class{\to }_{𝑔}$$
7	3	cv	$$setvarv$$
8	5 7 6	co	$$class\left(\left[{\neg }_{𝑔}u\right]{\to }_{𝑔}v\right)$$
9	1 3 2 2 8	cmpo	$$class\left(u\in \mathrm{V},v\in \mathrm{V}⟼\left[{\neg }_{𝑔}u\right]{\to }_{𝑔}v\right)$$
10	0 9	wceq	$$wff{\vee }_{𝑔}=\left(u\in \mathrm{V},v\in \mathrm{V}⟼\left[{\neg }_{𝑔}u\right]{\to }_{𝑔}v\right)$$