Theorem nftru 1395

Description: The true constant has no free variables. (This can also be proven in one step with nfv 1461, but this proof does not use ax-17 1459.) (Contributed by Mario Carneiro, 6-Oct-2016.)

Assertion

Ref	Expression
nftru	⊢ Ⅎ𝑥⊤

Proof of Theorem nftru

Step	Hyp	Ref	Expression
1		tru 1288	. 2 ⊢ ⊤
2	1	nfth 1393	1 ⊢ Ⅎ𝑥⊤

Syntax hints:  ⊤wtru 1285  Ⅎwnf 1389

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-gen 1378

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390

This theorem is referenced by:  nfmo  1961  dvelimc  2239  nfralxy  2402  nfrexxy  2403  nfralya  2404  nfrexya  2405  nfreuxy  2528  nfsbc  2835  nfcsb  2940  nfiotaxy  4891  nfriota  5497