Theorem truan 1331

Description: True can be removed from a conjunction. (Contributed by FL, 20-Mar-2011.)

Assertion

Ref	Expression
truan	⊢ (( ⊤ ∧ φ) ↔ φ)

Proof of Theorem truan

Step	Hyp	Ref	Expression
1		simpr 447	. 2 ⊢ (( ⊤ ∧ φ) → φ)
2		a1tru 1330	. . 3 ⊢ (φ → ⊤ )
3	2	ancri 535	. 2 ⊢ (φ → ( ⊤ ∧ φ))
4	1, 3	impbii 180	1 ⊢ (( ⊤ ∧ φ) ↔ φ)

This proof depends on syntax axioms:   ↔ wb 176   ∧ wa 358   ⊤ 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-an 360  df-tru 1319

This theorem is used by: (None)