Theorem nftru 1512

Description: The true constant has no free variables. (This can also be proven in one step with nfv 1574, but this proof does not use ax-17 1572.) (Contributed by Mario Carneiro, 6-Oct-2016.)

Assertion

Ref	Expression
nftru	⊢ Ⅎ𝑥⊤

Proof of Theorem nftru

Step	Hyp	Ref	Expression
1		tru 1399	. 2 ⊢ ⊤
2	1	nfth 1510	1 ⊢ Ⅎ𝑥⊤

Syntax hints:  ⊤wtru 1396  Ⅎwnf 1506

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 1495

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507

This theorem is referenced by:  nfmo  2097  dvelimc  2394  nfralw  2567  nfralxy  2568  nfrexw  2569  nfralya  2570  nfrexya  2571  nfreuw  2706  nfsbc  3049  nfsbcw  3159  nfcsbw  3161  nfcsb  3162  nfiotaw  5281  nfriota  5963  nfixpxy  6862