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Theorem truan 1302
Description: True can be removed from a conjunction. (Contributed by FL, 20-Mar-2011.) (Proof shortened by Wolf Lammen, 21-Jul-2019.)
Assertion
Ref Expression
truan  |-  ( ( T.  /\  ph )  <->  ph )

Proof of Theorem truan
StepHypRef Expression
1 tru 1289 . . 3  |- T.
21biantrur 297 . 2  |-  ( ph  <->  ( T.  /\  ph )
)
32bicomi 130 1  |-  ( ( T.  /\  ph )  <->  ph )
Colors of variables: wff set class
Syntax hints:    /\ wa 102    <-> wb 103   T. wtru 1286
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-tru 1288
This theorem is referenced by:  truanfal  1334  truxortru  1351  truxorfal  1352
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