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Theorem axlll2 25028
Description: One can add or remove a box in front of  x  =  y. (For my private use only. Don't use.) (Contributed by FL, 16-Sep-2016.)
Assertion
Ref Expression
axlll2  |-  ( [.] x  =  y  <->  x  =  y )

Proof of Theorem axlll2
StepHypRef Expression
1 alneal1 25000 . 2  |-  ( [.] x  =  y  ->  x  =  y )
2 ax-lll 25027 . 2  |-  ( x  =  y  ->  [.] x  =  y )
31, 2impbii 180 1  |-  ( [.] x  =  y  <->  x  =  y )
Colors of variables: wff set class
Syntax hints:    <-> wb 176   [.]wbox 24970
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-ltl1 24974  ax-ltl2 24975  ax-ltl3 24976  ax-ltl4 24977  ax-lmp 24978  ax-nmp 24979  ax-ltl5 24993  ax-ltl6 24994  ax-lll 25027
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-dia 24980
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