Theorem tru 1402

Description: The truth value T. is provable. (Contributed by Anthony Hart, 13-Oct-2010.)

Assertion

Ref	Expression
tru	|- T.

Proof of Theorem tru

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( A. x x = x -> A. x x = x )
2		df-tru 1401	. 2 |- ( T. <-> ( A. x x = x -> A. x x = x ) )
3	1, 2	mpbir 146	1 |- T.

Syntax hints:   -> wi 4   A.wal 1396   = wceq 1398   T. wtru 1399

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-tru 1401

This theorem is referenced by:  fal  1405  dftru2  1406  mptru  1407  tbtru  1408  bitru  1410  trud  1414  truan  1415  truorfal  1451  falortru  1452  truimfal  1455  nftru  1515  euotd  4371  rabxfr  4591  reuhyp  4593  elabrex  5930  elabrexg  5931  caovcl  6209  caovass  6215  caovdi  6234  ectocl  6836  reef11  12385  mpomulcn  15431  bj-sbimeh  16544  bdtru  16602  bj-nn0suc0  16720