Theorem nftru 1459

Description: The true constant has no free variables. (This can also be proven in one step with nfv 1521, but this proof does not use ax-17 1519.) (Contributed by Mario Carneiro, 6-Oct-2016.)

Assertion

Ref	Expression
nftru	⊢ Ⅎ𝑥⊤

Proof of Theorem nftru

Step	Hyp	Ref	Expression
1		tru 1352	. 2 ⊢ ⊤
2	1	nfth 1457	1 ⊢ Ⅎ𝑥⊤

Syntax hints:  ⊤wtru 1349  Ⅎwnf 1453

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 1442

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454

This theorem is referenced by:  nfmo  2039  dvelimc  2334  nfralw  2507  nfralxy  2508  nfrexxy  2509  nfralya  2510  nfrexya  2511  nfreuxy  2644  nfsbc  2975  nfcsbw  3085  nfcsb  3086  nfiotaw  5164  nfriota  5818  nfixpxy  6695