Theorem nfth 1517

Description: No variable is (effectively) free in a theorem. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
hbth.1	|- ph

Assertion

Ref	Expression
nfth	|- F/ x ph

Proof of Theorem nfth

Step	Hyp	Ref	Expression
1		hbth.1	. . 3 |- ph
2	1	hbth 1516	. 2 |- ( ph -> A. x ph )
3	2	nfi 1515	1 |- F/ x ph

This proof depends on syntax axioms:   F/wnf 1513

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1502

This proof depends on definitions:  df-bi 117  df-nf 1514

This theorem is used by:  nftru  1519  nfequid  1754  sbt  1837  sbc2ie  3123  omsinds  4769