Definition df-goim

Description: Define the Godel-set of implication. 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-goim	$$⊢{\to }_{𝑔}=\left(u\in \mathrm{V},v\in \mathrm{V}⟼u{⊼}_{𝑔}\left[{\neg }_{𝑔}v\right]\right)$$

Detailed syntax breakdown

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