Theorem nftru 1477

Description: The true constant has no free variables. (This can also be proven in one step with nfv 1539, but this proof does not use ax-17 1537.) (Contributed by Mario Carneiro, 6-Oct-2016.)

Assertion

Ref	Expression
nftru	⊢ Ⅎ𝑥⊤

Proof of Theorem nftru

Step	Hyp	Ref	Expression
1		tru 1368	. 2 ⊢ ⊤
2	1	nfth 1475	1 ⊢ Ⅎ𝑥⊤

Syntax hints:  ⊤wtru 1365  Ⅎwnf 1471

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 1460

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472

This theorem is referenced by:  nfmo  2062  dvelimc  2358  nfralw  2531  nfralxy  2532  nfrexw  2533  nfralya  2534  nfrexya  2535  nfreuxy  2669  nfsbc  3006  nfsbcw  3115  nfcsbw  3117  nfcsb  3118  nfiotaw  5219  nfriota  5883  nfixpxy  6771