Theorem nftru 1454

Description: The true constant has no free variables. (This can also be proven in one step with nfv 1516, but this proof does not use ax-17 1514.) (Contributed by Mario Carneiro, 6-Oct-2016.)

Assertion

Ref	Expression
nftru	⊢ Ⅎ𝑥⊤

Proof of Theorem nftru

Step	Hyp	Ref	Expression
1		tru 1347	. 2 ⊢ ⊤
2	1	nfth 1452	1 ⊢ Ⅎ𝑥⊤

Syntax hints:  ⊤wtru 1344  Ⅎwnf 1448

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 1437

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449

This theorem is referenced by:  nfmo  2034  dvelimc  2330  nfralw  2503  nfralxy  2504  nfrexxy  2505  nfralya  2506  nfrexya  2507  nfreuxy  2640  nfsbc  2971  nfcsbw  3081  nfcsb  3082  nfiotaw  5157  nfriota  5807  nfixpxy  6683