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	⊢ →𝑔 = ( 𝑢 ∈ V , 𝑣 ∈ V ↦ ( 𝑢 ⊼𝑔 ¬𝑔 𝑣 ) )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cgoi	⊢ →𝑔
1		vu	⊢ 𝑢
2		cvv	⊢ V
3		vv	⊢ 𝑣
4	1	cv	⊢ 𝑢
5		cgna	⊢ ⊼𝑔
6	3	cv	⊢ 𝑣
7	6	cgon	⊢ ¬𝑔 𝑣
8	4 7 5	co	⊢ ( 𝑢 ⊼𝑔 ¬𝑔 𝑣 )
9	1 3 2 2 8	cmpo	⊢ ( 𝑢 ∈ V , 𝑣 ∈ V ↦ ( 𝑢 ⊼𝑔 ¬𝑔 𝑣 ) )
10	0 9	wceq	⊢ →𝑔 = ( 𝑢 ∈ V , 𝑣 ∈ V ↦ ( 𝑢 ⊼𝑔 ¬𝑔 𝑣 ) )