Theorem trud 1550

Description: Anything implies ⊤. Dual statement of falim 1557. Deduction form of tru 1544. Note on naming: in 2022, the theorem now known as mptru 1547 was renamed from trud so if you are reading documentation written before that time, references to trud refer to what is now mptru 1547. (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 1544	. 2 ⊢ ⊤
2	1	a1i 11	1 ⊢ (𝜑 → ⊤)

Syntax hints:   → wi 4  ⊤wtru 1541

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 1543

This theorem is referenced by:  falimtru  1565  emptyex  1907  disjprg  5103  euotd  5473  elabrex  7216  elabrexg  7217  riota5f  7372  bj-abv  36894  wl-2mintru1  37478  wl-nax6im  37506  ac6s6  38166  lhpexle1  40002  prjspvs  42598  cnvtrucl0  43613  rfovcnvf1od  43993  fsupdm  46840  thinciso  49459