Theorem a1tru 1330

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 1321	. 2 ⊢ ⊤
2	1	a1i 10	1 ⊢ (φ → ⊤ )

This proof depends on syntax axioms:   → wi 4   ⊤ wtru 1316

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-tru 1319

This theorem is used by:  truan  1331