Theorem bcxmaslem1 12233

Description: Lemma for bcxmas 12234. (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 6083	. 2 |- ( A = B -> ( N + A ) = ( N + B ) )
2		id 19	. 2 |- ( A = B -> A = B )
3	1, 2	oveq12d 6093	1 |- ( A = B -> ( ( N + A ) _C A ) = ( ( N + B ) _C B ) )

Syntax hints:   -> wi 4   = wceq 1402  (class class class)co 6075   + caddc 8172   _C cbc 11163

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-3an 1011  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-rex 2534  df-v 2823  df-un 3224  df-sn 3711  df-pr 3712  df-op 3714  df-uni 3931  df-br 4126  df-iota 5332  df-fv 5380  df-ov 6078

This theorem is referenced by:  bcxmas  12234