Theorem difeq2i 2156

Description: Inference adding difference to the left in a class equality.

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 2154	. 2 |- (A = B -> (C \ A) = (C \ B))
3	1, 2	ax-mp 7	1 |- (C \ A) = (C \ B)

Syntax hints:   = wceq 956   \ cdif 2044

This theorem is referenced by:  difeq12i 2157  dfun3 2246  dfin3 2247  dfin4 2248  invdif 2249  indif 2250  difundi 2257  difindi 2259  dif23 2264  symdif1 2265  dif0 2335  undifv 2339  difdifdir 2346  dfsdom2 4460  numthlem 4783

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-dif 2049

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