Theorem bcxmaslem1 10945

Description: Lemma for bcxmas 10946. (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

Step	Hyp	Ref	Expression
1		oveq2 5676	. 2 |- ( A = B -> ( N + A ) = ( N + B ) )
2		id 19	. 2 |- ( A = B -> A = B )
3	1, 2	oveq12d 5686	1 |- ( A = B -> ( ( N + A ) _C A ) = ( ( N + B ) _C B ) )

Syntax hints:   -> wi 4   = wceq 1290  (class class class)co 5668   + caddc 7416   _C cbc 10218

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071

This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-rex 2366  df-v 2624  df-un 3006  df-sn 3458  df-pr 3459  df-op 3461  df-uni 3662  df-br 3854  df-iota 4995  df-fv 5038  df-ov 5671

This theorem is referenced by:  bcxmas  10946