Theorem a1tru 1347

Description: Anything implies ⊤. (Contributed by FL, 20-Mar-2011.) (Proof shortened by Anthony Hart, 1-Aug-2011.)

Assertion

Ref	Expression
a1tru	⊢ (𝜑 → ⊤)

Proof of Theorem a1tru

Step	Hyp	Ref	Expression
1		tru 1335	. 2 ⊢ ⊤
2	1	a1i 9	1 ⊢ (𝜑 → ⊤)

Syntax hints:   → wi 4  ⊤wtru 1332

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-tru 1334

This theorem is referenced by:  euotd  4171  elabrex  5652  riota5f  5747  bj-nn0suc0  13137