Theorem nftru 1442

Description: The true constant has no free variables. (This can also be proven in one step with nfv 1508, but this proof does not use ax-17 1506.) (Contributed by Mario Carneiro, 6-Oct-2016.)

Assertion

Ref	Expression
nftru	⊢ Ⅎ𝑥⊤

Proof of Theorem nftru

Step	Hyp	Ref	Expression
1		tru 1335	. 2 ⊢ ⊤
2	1	nfth 1440	1 ⊢ Ⅎ𝑥⊤

Syntax hints:  ⊤wtru 1332  Ⅎwnf 1436

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-gen 1425

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437

This theorem is referenced by:  nfmo  2019  dvelimc  2302  nfralxy  2471  nfrexxy  2472  nfralya  2473  nfrexya  2474  nfreuxy  2605  nfsbc  2929  nfcsb  3037  nfiotaw  5092  nfriota  5739  nfixpxy  6611