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Theorem bcxmaslem1 12308
Description: Lemma for bcxmas 12310. (Contributed by Paul Chapman, 18-May-2007.)
Assertion
Ref Expression
bcxmaslem1  |-  ( A  =  B  ->  (
( N  +  A
)  _C  A )  =  ( ( N  +  B )  _C  B ) )

Proof of Theorem bcxmaslem1
StepHypRef Expression
1 oveq2 5882 . 2  |-  ( A  =  B  ->  ( N  +  A )  =  ( N  +  B ) )
2 id 19 . 2  |-  ( A  =  B  ->  A  =  B )
31, 2oveq12d 5892 1  |-  ( A  =  B  ->  (
( N  +  A
)  _C  A )  =  ( ( N  +  B )  _C  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1632  (class class class)co 5874    + caddc 8756    _C cbc 11331
This theorem is referenced by:  bcxmas  12310  sylow1lem1  14925
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-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279  df-ov 5877
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