Theorem ineq1i 2213

Description: Equality inference for intersection of two classes.

Hypothesis

Ref	Expression
ineq1i.1	|- A = B

Assertion

Ref	Expression
ineq1i	|- (A i^i C) = (B i^i C)

Proof of Theorem ineq1i

Step	Hyp	Ref	Expression
1		ineq1i.1	. 2 |- A = B
2		ineq1 2210	. 2 |- (A = B -> (A i^i C) = (B i^i C))
3	1, 2	ax-mp 7	1 |- (A i^i C) = (B i^i C)

Syntax hints:   = wceq 956   i^i cin 2046

This theorem is referenced by:  in12 2224  inindi 2227  dfrab2 2274  resres 3377  resdisj 3471  rescnvcnv 3493  ssenen 4504  chdmj2 9405  chjass 9409  pjoml2 9528  pjoml4 9530  cmcmlem 9534  cvmd 10251  atoml 10309  atabs 10328

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-v 1812  df-in 2051

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