Theorem difeq2i 3296

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

Hypothesis

Ref	Expression
difeq1i.1	|- A = B

Assertion

Ref	Expression
difeq2i	|- ( C \ A ) = ( C \ B )

Proof of Theorem difeq2i

Step	Hyp	Ref	Expression
1		difeq1i.1	. 2 |- A = B
2		difeq2 3293	. 2 |- ( A = B -> ( C \ A ) = ( C \ B ) )
3	1, 2	ax-mp 5	1 |- ( C \ A ) = ( C \ B )

Syntax hints:   = wceq 1373   \ cdif 3171

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-in1 615  ax-in2 616  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-ral 2491  df-rab 2495  df-dif 3176

This theorem is referenced by:  difeq12i  3297  inssddif  3422  difdif2ss  3438  dif32  3444  difabs  3445  symdif1  3446  notrab  3458  dif0  3539  difdifdirss  3553  dfif3  3593  difpr  3786  dif1o  6547  unfiin  7049  m1bits  12386