Theorem difeq1i 3318

Description: Inference adding difference to the right in a class equality. (Contributed by NM, 15-Nov-2002.)

Hypothesis

Ref	Expression
difeq1i.1	|- A = B

Assertion

Ref	Expression
difeq1i	|- ( A \ C ) = ( B \ C )

Proof of Theorem difeq1i

Step	Hyp	Ref	Expression
1		difeq1i.1	. 2 |- A = B
2		difeq1 3315	. 2 |- ( A = B -> ( A \ C ) = ( B \ C ) )
3	1, 2	ax-mp 5	1 |- ( A \ C ) = ( B \ C )

Syntax hints:   = wceq 1395   \ cdif 3194

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-rab 2517  df-dif 3199

This theorem is referenced by:  difeq12i  3320  indif1  3449  indifcom  3450  difun1  3464  notab  3474  notrab  3481  difprsn1  3807  difprsn2  3808  orddif  4639  resdifcom  5023  resdmdfsn  5048  phplem1  7013  dfn2  9382