Theorem nftru 1407

Description: The true constant has no free variables. (This can also be proven in one step with nfv 1473, but this proof does not use ax-17 1471.) (Contributed by Mario Carneiro, 6-Oct-2016.)

Assertion

Ref	Expression
nftru	⊢ Ⅎ𝑥⊤

Proof of Theorem nftru

Step	Hyp	Ref	Expression
1		tru 1300	. 2 ⊢ ⊤
2	1	nfth 1405	1 ⊢ Ⅎ𝑥⊤

Syntax hints:  ⊤wtru 1297  Ⅎwnf 1401

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1390

This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402

This theorem is referenced by:  nfmo  1975  dvelimc  2256  nfralxy  2425  nfrexxy  2426  nfralya  2427  nfrexya  2428  nfreuxy  2555  nfsbc  2874  nfcsb  2979  nfiotaxy  5018  nfriota  5655  nfixpxy  6514