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Theorem bcxmaslem1 12576
Description: Lemma for bcxmas 12578. (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 6056 . 2  |-  ( A  =  B  ->  ( N  +  A )  =  ( N  +  B ) )
2 id 20 . 2  |-  ( A  =  B  ->  A  =  B )
31, 2oveq12d 6066 1  |-  ( A  =  B  ->  (
( N  +  A
)  _C  A )  =  ( ( N  +  B )  _C  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649  (class class class)co 6048    + caddc 8957    _C cbc 11556
This theorem is referenced by:  bcxmas  12578  sylow1lem1  15195
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-rex 2680  df-rab 2683  df-v 2926  df-dif 3291  df-un 3293  df-in 3295  df-ss 3302  df-nul 3597  df-if 3708  df-sn 3788  df-pr 3789  df-op 3791  df-uni 3984  df-br 4181  df-iota 5385  df-fv 5429  df-ov 6051
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