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Theorem bnj1322 28855
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj1322  |-  ( A  =  B  ->  ( A  i^i  B )  =  A )

Proof of Theorem bnj1322
StepHypRef Expression
1 eqimss 3230 . 2  |-  ( A  =  B  ->  A  C_  B )
2 df-ss 3166 . 2  |-  ( A 
C_  B  <->  ( A  i^i  B )  =  A )
31, 2sylib 188 1  |-  ( A  =  B  ->  ( A  i^i  B )  =  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623    i^i cin 3151    C_ wss 3152
This theorem is referenced by:  bnj1321  29057
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-in 3159  df-ss 3166
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