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Theorem axlll2 25131
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 25103 . 2  |-  ( [.] x  =  y  ->  x  =  y )
2 ax-lll 25130 . 2  |-  ( x  =  y  ->  [.] x  =  y )
31, 2impbii 180 1  |-  ( [.] x  =  y  <->  x  =  y )
Colors of variables: wff set class
Syntax hints:    <-> wb 176   [.]wbox 25073
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-ltl1 25077  ax-ltl2 25078  ax-ltl3 25079  ax-ltl4 25080  ax-lmp 25081  ax-nmp 25082  ax-ltl5 25096  ax-ltl6 25097  ax-lll 25130
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-dia 25083
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