Theorem trud 1551

Description: Anything implies ⊤. Dual statement of falim 1558. Deduction form of tru 1545. Note on naming: in 2022, the theorem now known as mptru 1548 was renamed from trud so if you are reading documentation written before that time, references to trud refer to what is now mptru 1548. (Contributed by FL, 20-Mar-2011.) (Proof shortened by Anthony Hart, 1-Aug-2011.)

Assertion

Ref	Expression
trud	⊢ (𝜑 → ⊤)

Proof of Theorem trud

Step	Hyp	Ref	Expression
1		tru 1545	. 2 ⊢ ⊤
2	1	a1i 11	1 ⊢ (𝜑 → ⊤)

Syntax hints:   → wi 4  ⊤wtru 1542

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-tru 1544

This theorem is referenced by:  falimtru  1566  emptyex  1908  disjprg  5087  euotd  5453  elabrex  7176  elabrexg  7177  riota5f  7331  bj-abv  36946  wl-2mintru1  37530  wl-nax6im  37558  ac6s6  38218  lhpexle1  40053  prjspvs  42649  cnvtrucl0  43663  rfovcnvf1od  44043  fsupdm  46886  thinciso  49508