Theorem nftru 1355

Description: The true constant has no free variables. (This can also be proven in one step with nfv 1421, but this proof does not use ax-17 1419.) (Contributed by Mario Carneiro, 6-Oct-2016.)

Assertion

Ref	Expression
nftru	⊢ Ⅎ𝑥⊤

Proof of Theorem nftru

Step	Hyp	Ref	Expression
1		tru 1247	. 2 ⊢ ⊤
2	1	nfth 1353	1 ⊢ Ⅎ𝑥⊤

Syntax hints:  ⊤wtru 1244  Ⅎwnf 1349

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1338

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350

This theorem is referenced by:  nfmo  1920  dvelimc  2198  nfralxy  2360  nfrexxy  2361  nfralya  2362  nfrexya  2363  nfreuxy  2484  nfsbc  2784  nfcsb  2884  nfiotaxy  4871  nfriota  5477