Theorem tru 1402

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

Assertion

Ref	Expression
tru	⊢ ⊤

Proof of Theorem tru

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (∀𝑥 𝑥 = 𝑥 → ∀𝑥 𝑥 = 𝑥)
2		df-tru 1401	. 2 ⊢ (⊤ ↔ (∀𝑥 𝑥 = 𝑥 → ∀𝑥 𝑥 = 𝑥))
3	1, 2	mpbir 146	1 ⊢ ⊤

Syntax hints:   → wi 4  ∀wal 1396   = wceq 1398  ⊤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  4376  rabxfr  4596  reuhyp  4598  elabrex  5936  elabrexg  5937  caovcl  6217  caovass  6223  caovdi  6242  ectocl  6849  reef11  12410  mpomulcn  15557  bj-sbimeh  16670  bdtru  16728  bj-nn0suc0  16846