Theorem difeq12i 3244

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 3242	. 2 |- ( A \ C ) = ( B \ C )
3		difeq12i.2	. . 3 |- C = D
4	3	difeq2i 3243	. 2 |- ( B \ C ) = ( B \ D )
5	2, 4	eqtri 2192	1 |- ( A \ C ) = ( B \ D )

Syntax hints:   = wceq 1349   \ cdif 3119

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 610  ax-in2 611  ax-io 705  ax-5 1441  ax-7 1442  ax-gen 1443  ax-ie1 1487  ax-ie2 1488  ax-8 1498  ax-10 1499  ax-11 1500  ax-i12 1501  ax-bndl 1503  ax-4 1504  ax-17 1520  ax-i9 1524  ax-ial 1528  ax-i5r 1529  ax-ext 2153

This theorem depends on definitions:  df-bi 116  df-tru 1352  df-nf 1455  df-sb 1757  df-clab 2158  df-cleq 2164  df-clel 2167  df-nfc 2302  df-ral 2454  df-rab 2458  df-dif 3124

This theorem is referenced by:  difrab  3402  imadiflem  5279  imadif  5280