Theorem nftru 1514

Description: The true constant has no free variables. (This can also be proven in one step with nfv 1576, but this proof does not use ax-17 1574.) (Contributed by Mario Carneiro, 6-Oct-2016.)

Assertion

Ref	Expression
nftru	⊢ Ⅎ𝑥⊤

Proof of Theorem nftru

Step	Hyp	Ref	Expression
1		tru 1401	. 2 ⊢ ⊤
2	1	nfth 1512	1 ⊢ Ⅎ𝑥⊤

Syntax hints:  ⊤wtru 1398  Ⅎwnf 1508

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 1497

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509

This theorem is referenced by:  nfmo  2099  dvelimc  2396  nfralw  2569  nfralxy  2570  nfrexw  2571  nfralya  2572  nfrexya  2573  nfreuw  2708  nfsbc  3052  nfsbcw  3162  nfcsbw  3164  nfcsb  3165  nfiotaw  5290  nfriota  5980  nfixpxy  6885