Theorem nftru 1490

Description: The true constant has no free variables. (This can also be proven in one step with nfv 1552, but this proof does not use ax-17 1550.) (Contributed by Mario Carneiro, 6-Oct-2016.)

Assertion

Ref	Expression
nftru	⊢ Ⅎ𝑥⊤

Proof of Theorem nftru

Step	Hyp	Ref	Expression
1		tru 1377	. 2 ⊢ ⊤
2	1	nfth 1488	1 ⊢ Ⅎ𝑥⊤

Syntax hints:  ⊤wtru 1374  Ⅎwnf 1484

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 1473

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485

This theorem is referenced by:  nfmo  2075  dvelimc  2371  nfralw  2544  nfralxy  2545  nfrexw  2546  nfralya  2547  nfrexya  2548  nfreuxy  2682  nfsbc  3023  nfsbcw  3132  nfcsbw  3134  nfcsb  3135  nfiotaw  5245  nfriota  5922  nfixpxy  6817