Theorem trud 1648

Description: Anything implies ⊤. Dual statement of falim 1655. (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 1642	. 2 ⊢ ⊤
2	1	a1i 11	1 ⊢ (𝜑 → ⊤)

Syntax hints:   → wi 4  ⊤wtru 1638

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 198  df-tru 1641

This theorem is referenced by:  falimtru  1663  disjprg  4840  euotd  5168  mptexgf  6706  elabrex  6721  riota5f  6856  ac6s6  34285  lhpexle1  35783  cnvtrucl0  38425  rfovcnvf1od  38792  elabrexg  39694