Theorem nftru 1515

Description: The true constant has no free variables. (This can also be proven in one step with nfv 1577, but this proof does not use ax-17 1575.) (Contributed by Mario Carneiro, 6-Oct-2016.)

Assertion

Ref	Expression
nftru	⊢ Ⅎ𝑥⊤

Proof of Theorem nftru

Step	Hyp	Ref	Expression
1		tru 1402	. 2 ⊢ ⊤
2	1	nfth 1513	1 ⊢ Ⅎ𝑥⊤

Syntax hints:  ⊤wtru 1399  Ⅎwnf 1509

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1498

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510

This theorem is referenced by:  nfmo  2102  dvelimc  2408  nfralw  2581  nfralxy  2582  nfrexw  2583  nfralya  2584  nfrexya  2585  nfreuw  2720  nfsbc  3065  nfsbcw  3175  nfcsbw  3177  nfcsb  3178  nfiotaw  5318  nfriota  6015  nfixpxy  6954