Theorem truan 1331

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

Assertion

Ref	Expression
truan	|- (( T. /\ ph) <-> ph)

Proof of Theorem truan

Step	Hyp	Ref	Expression
1		simpr 447	. 2 |- (( T. /\ ph) -> ph)
2		a1tru 1330	. . 3 |- (ph -> T. )
3	2	ancri 535	. 2 |- (ph -> ( T. /\ ph))
4	1, 3	impbii 180	1 |- (( T. /\ ph) <-> ph)

This proof depends on syntax axioms:   <-> wb 176   /\ wa 358   T. 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)