Theorem difeq2i 3288

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 3285	. 2 |- ( A = B -> ( C \ A ) = ( C \ B ) )
3	1, 2	ax-mp 5	1 |- ( C \ A ) = ( C \ B )

Syntax hints:   = wceq 1373   \ cdif 3163

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-11 1529  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-ral 2489  df-rab 2493  df-dif 3168

This theorem is referenced by:  difeq12i  3289  inssddif  3414  difdif2ss  3430  dif32  3436  difabs  3437  symdif1  3438  notrab  3450  dif0  3531  difdifdirss  3545  dfif3  3584  difpr  3775  dif1o  6524  unfiin  7023  m1bits  12271