Theorem a1tru 1259

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 1247	. 2 ⊢ ⊤
2	1	a1i 9	1 ⊢ (𝜑 → ⊤)

Syntax hints:   → wi 4  ⊤wtru 1244

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-tru 1246

This theorem is referenced by:  truanOLD  1261  euotd  3991  elabrex  5397  riota5f  5492  bj-nn0suc0  10075