Theorem bcxmaslem1 11496

Description: Lemma for bcxmas 11497. (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 5883	. 2 |- ( A = B -> ( N + A ) = ( N + B ) )
2		id 19	. 2 |- ( A = B -> A = B )
3	1, 2	oveq12d 5893	1 |- ( A = B -> ( ( N + A ) _C A ) = ( ( N + B ) _C B ) )

Syntax hints:   -> wi 4   = wceq 1353  (class class class)co 5875   + caddc 7814   _C cbc 10727

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rex 2461  df-v 2740  df-un 3134  df-sn 3599  df-pr 3600  df-op 3602  df-uni 3811  df-br 4005  df-iota 5179  df-fv 5225  df-ov 5878

This theorem is referenced by:  bcxmas  11497