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Theorem bcxmaslem1 12651
Description: Lemma for bcxmas 12653. (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 6125 . 2  |-  ( A  =  B  ->  ( N  +  A )  =  ( N  +  B ) )
2 id 21 . 2  |-  ( A  =  B  ->  A  =  B )
31, 2oveq12d 6135 1  |-  ( A  =  B  ->  (
( N  +  A
)  _C  A )  =  ( ( N  +  B )  _C  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1654  (class class class)co 6117    + caddc 9031    _C cbc 11631
This theorem is referenced by:  bcxmas  12653  sylow1lem1  15270
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-rex 2718  df-rab 2721  df-v 2967  df-dif 3312  df-un 3314  df-in 3316  df-ss 3323  df-nul 3617  df-if 3768  df-sn 3849  df-pr 3850  df-op 3852  df-uni 4045  df-br 4244  df-iota 5453  df-fv 5497  df-ov 6120
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