Theorem nfnth 1458

Description: No variable is (effectively) free in a non-theorem. (Contributed by Mario Carneiro, 6-Dec-2016.)

Hypothesis

Ref	Expression
nfnth.1	|- -. ph

Assertion

Ref	Expression
nfnth	|- F/ x ph

Proof of Theorem nfnth

Step	Hyp	Ref	Expression
1		nfnth.1	. . 3 |- -. ph
2	1	pm2.21i 641	. 2 |- ( ph -> A. x ph )
3	2	nfi 1455	1 |- F/ x ph

Syntax hints:   -. wn 3   A.wal 1346   F/wnf 1453

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 610  ax-gen 1442

This theorem depends on definitions:  df-bi 116  df-nf 1454

This theorem is referenced by: (None)