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Metamath Proof Explorer

Definition df-gonot

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

		Ref	Expression
	Assertion	df-gonot	⊢ ¬_𝑔 𝑈 = ( 𝑈 ⊼_𝑔 𝑈 )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cU	⊢ 𝑈
1	0	cgon	⊢ ¬_𝑔 𝑈
2		cgna	⊢ ⊼_𝑔
3	0 0 2	co	⊢ ( 𝑈 ⊼_𝑔 𝑈 )
4	1 3	wceq	⊢ ¬_𝑔 𝑈 = ( 𝑈 ⊼_𝑔 𝑈 )