Theorem nftru 1519

Description: The true constant has no free variables. (This can also be proven in one step with nfv 1581, but this proof does not use ax-17 1579.) (Contributed by Mario Carneiro, 6-Oct-2016.)

Assertion

Ref	Expression
nftru	⊢ Ⅎ𝑥⊤

Proof of Theorem nftru

Step	Hyp	Ref	Expression
1		tru 1406	. 2 ⊢ ⊤
2	1	nfth 1517	1 ⊢ Ⅎ𝑥⊤

Syntax hints:  ⊤wtru 1403  Ⅎwnf 1513

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 1502

This theorem depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514

This theorem is referenced by:  nfmo  2106  dvelimc  2414  nfralw  2587  nfralxy  2588  nfrexw  2589  nfralya  2590  nfrexya  2591  nfreuw  2726  nfsbc  3072  nfsbcw  3182  nfcsbw  3184  nfcsb  3185  nfiotaw  5336  nfriota  6038  nfixpxy  6989