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Theorem bnj1322 29171
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 3243 . 2  |-  ( A  =  B  ->  A  C_  B )
2 df-ss 3179 . 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 1632    i^i cin 3164    C_ wss 3165
This theorem is referenced by:  bnj1321  29373
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-in 3172  df-ss 3179
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