MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  a1tru Structured version   Visualization version   GIF version

Theorem a1tru 1497
Description: Anything implies . (Contributed by FL, 20-Mar-2011.) (Proof shortened by Anthony Hart, 1-Aug-2011.)
Assertion
Ref Expression
a1tru (𝜑 → ⊤)

Proof of Theorem a1tru
StepHypRef Expression
1 tru 1484 . 2
21a1i 11 1 (𝜑 → ⊤)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wtru 1481
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 197  df-tru 1483
This theorem is referenced by:  disjprg  4610  euotd  4937  mptexgf  6442  elabrex  6458  riota5f  6593  ac6s6  33633  lhpexle1  34795  cnvtrucl0  37433  rfovcnvf1od  37801  elabrexg  38710
  Copyright terms: Public domain W3C validator