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 207  df-tru 1545

This theorem is referenced by:  falimtru  1567  emptyex  1909  disjprg  5096  euotd  5469  elabrex  7198  elabrexg  7199  riota5f  7353  bj-exextruan  36875  bj-cbvew  36879  bj-abv  37148  wl-2mintru1  37739  wl-nax6im  37767  ac6s6  38417  lhpexle1  40378  prjspvs  42962  cnvtrucl0  43974  rfovcnvf1od  44354  fsupdm  47194  thinciso  49823