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 209  df-tru 1540

This theorem is referenced by:  falimtru  1562  emptyex  1908  disjprgw  5061  disjprg  5062  euotd  5403  mptexgf  6985  elabrex  7002  riota5f  7142  wl-nax6im  34773  ac6s6  35465  lhpexle1  37159  prjspvs  39280  cnvtrucl0  40004  rfovcnvf1od  40370  elabrexg  41323