Theorem trud 1418

Description: Anything implies ⊤. (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 1406	. 2 ⊢ ⊤
2	1	a1i 9	1 ⊢ (𝜑 → ⊤)

This proof depends on syntax axioms:   → wi 4  ⊤wtru 1403

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-tru 1405

This theorem is used by:  euotd  4395  elabrex  5963  elabrexg  5964  riota5f  6065  bj-nn0suc0  16988