Theorem difeq12i 3266

Description: Equality inference for class difference. (Contributed by NM, 29-Aug-2004.)

Hypotheses

Ref	Expression
difeq1i.1	|- A = B
difeq12i.2	|- C = D

Assertion

Ref	Expression
difeq12i	|- ( A \ C ) = ( B \ D )

Proof of Theorem difeq12i

Step	Hyp	Ref	Expression
1		difeq1i.1	. . 3 |- A = B
2	1	difeq1i 3264	. 2 |- ( A \ C ) = ( B \ C )
3		difeq12i.2	. . 3 |- C = D
4	3	difeq2i 3265	. 2 |- ( B \ C ) = ( B \ D )
5	2, 4	eqtri 2210	1 |- ( A \ C ) = ( B \ D )

Syntax hints:   = wceq 1364   \ cdif 3141

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-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-rab 2477  df-dif 3146

This theorem is referenced by:  difrab  3424  imadiflem  5314  imadif  5315