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  2099  dvelimc  2397  nfralw  2570  nfralxy  2571  nfrexw  2572  nfralya  2573  nfrexya  2574  nfreuw  2709  nfsbc  3053  nfsbcw  3163  nfcsbw  3165  nfcsb  3166  nfiotaw  5297  nfriota  5991  nfixpxy  6929