Theorem trud 1552

Description: Anything implies ⊤. Dual statement of falim 1559. Deduction form of tru 1546. Note on naming: in 2022, the theorem now known as mptru 1549 was renamed from trud so if you are reading documentation written before that time, references to trud refer to what is now mptru 1549. (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 1546	. 2 ⊢ ⊤
2	1	a1i 11	1 ⊢ (𝜑 → ⊤)

Syntax hints:   → wi 4  ⊤wtru 1543

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 206  df-tru 1545

This theorem is referenced by:  falimtru  1567  emptyex  1911  disjprgw  5144  disjprg  5145  euotd  5514  elabrex  7242  riota5f  7394  bj-abv  35786  wl-2mintru1  36371  wl-nax6im  36387  ac6s6  37040  lhpexle1  38879  prjspvs  41352  cnvtrucl0  42375  rfovcnvf1od  42755  elabrexg  43728  fsupdm  45558  thinciso  47680