Theorem trud 1547

Description: Anything implies ⊤. Dual statement of falim 1554. Deduction form of tru 1541. Note on naming: in 2022, the theorem now known as mptru 1544 was renamed from trud so if you are reading documentation written before that time, references to trud refer to what is now mptru 1544. (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 1541	. 2 ⊢ ⊤
2	1	a1i 11	1 ⊢ (𝜑 → ⊤)

Syntax hints:   → wi 4  ⊤wtru 1538

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 1540

This theorem is referenced by:  falimtru  1562  emptyex  1905  disjprg  5144  euotd  5523  elabrex  7262  elabrexg  7263  riota5f  7416  bj-abv  36889  wl-2mintru1  37473  wl-nax6im  37499  ac6s6  38159  lhpexle1  39991  prjspvs  42597  cnvtrucl0  43614  rfovcnvf1od  43994  fsupdm  46798  thinciso  48861