This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem nfth

Description: No variable is (effectively) free in a theorem. (Contributed by Mario Carneiro, 11-Aug-2016) df-nf changed. (Revised by Wolf Lammen, 12-Sep-2021)

		Ref	Expression
	Hypothesis	nfth.1	\|- ph
	Assertion	nfth	\|- F/ x ph

Proof

Step	Hyp	Ref	Expression
1		nfth.1	\|- ph
2		nftht	\|- ( A. x ph -> F/ x ph )
3	2 1	mpg	\|- F/ x ph