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  5081  euotd  5467  elabrex  7197  elabrexg  7198  riota5f  7352  bj-exextruan  36932  bj-cbvew  36936  bj-abv  37213  wl-2mintru1  37806  wl-nax6im  37843  ac6s6  38493  lhpexle1  40454  prjspvs  43043  cnvtrucl0  44051  rfovcnvf1od  44431  fsupdm  47270  thinciso  49945