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Theorem trujust 1291
Description: Soundness justification theorem for df-tru 1292. (Contributed by Mario Carneiro, 17-Nov-2013.) (Revised by NM, 11-Jul-2019.)
Assertion
Ref Expression
trujust  |-  ( ( A. x  x  =  x  ->  A. x  x  =  x )  <->  ( A. y  y  =  y  ->  A. y 
y  =  y ) )

Proof of Theorem trujust
StepHypRef Expression
1 id 19 . 2  |-  ( A. x  x  =  x  ->  A. x  x  =  x )
2 id 19 . 2  |-  ( A. y  y  =  y  ->  A. y  y  =  y )
31, 22th 172 1  |-  ( ( A. x  x  =  x  ->  A. x  x  =  x )  <->  ( A. y  y  =  y  ->  A. y 
y  =  y ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   A.wal 1287    = wceq 1289
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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