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  5089  euotd  5456  elabrex  7182  elabrexg  7183  riota5f  7337  bj-abv  36971  wl-2mintru1  37555  wl-nax6im  37583  ac6s6  38233  lhpexle1  40128  prjspvs  42729  cnvtrucl0  43742  rfovcnvf1od  44122  fsupdm  46965  thinciso  49596