Theorem trud 1551

Description: Anything implies ⊤. Dual statement of falim 1558. Deduction form of tru 1545. Note on naming: in 2022, the theorem now known as mptru 1548 was renamed from trud so if you are reading documentation written before that time, references to trud refer to what is now mptru 1548. (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 1545	. 2 ⊢ ⊤
2	1	a1i 11	1 ⊢ (𝜑 → ⊤)

Syntax hints:   → wi 4  ⊤wtru 1542

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 1544

This theorem is referenced by:  falimtru  1566  emptyex  1910  disjprgw  5105  disjprg  5106  euotd  5475  elabrex  7195  riota5f  7347  bj-abv  35449  wl-2mintru1  36034  wl-nax6im  36050  ac6s6  36704  lhpexle1  38544  prjspvs  41006  cnvtrucl0  42018  rfovcnvf1od  42398  elabrexg  43371  fsupdm  45203  thinciso  47200