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Theorem ineq2i 3129
Description: Equality inference for intersection of two classes. (Contributed by NM, 26-Dec-1993.)
Hypothesis
Ref Expression
ineq1i.1 A = B
Assertion
Ref Expression
ineq2i (𝐶A) = (𝐶B)

Proof of Theorem ineq2i
StepHypRef Expression
1 ineq1i.1 . 2 A = B
2 ineq2 3126 . 2 (A = B → (𝐶A) = (𝐶B))
31, 2ax-mp 7 1 (𝐶A) = (𝐶B)
Colors of variables: wff set class
Syntax hints:   = wceq 1242  cin 2910
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918
This theorem is referenced by:  in4  3147  inindir  3149  indif2  3175  difun1  3191  dfrab3ss  3209  dfif3  3337  intunsn  3644  rint0  3645  riin0  3719  res0  4559  resres  4567  resundi  4568  resindi  4570  inres  4572  resiun2  4574  resopab  4595  dfse2  4641  dminxp  4708  imainrect  4709  resdmres  4755  funimacnv  4918  dmaddpi  6309  dmmulpi  6310
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