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Theorem inteqd 3611
Description: Equality deduction for class intersection. (Contributed by NM, 2-Sep-2003.)
Hypothesis
Ref Expression
inteqd.1 (φA = B)
Assertion
Ref Expression
inteqd (φ A = B)

Proof of Theorem inteqd
StepHypRef Expression
1 inteqd.1 . 2 (φA = B)
2 inteq 3609 . 2 (A = B A = B)
31, 2syl 14 1 (φ A = B)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242   cint 3606
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-ral 2305  df-int 3607
This theorem is referenced by:  intprg  3639  op1stbg  4176  onsucmin  4198  elreldm  4503  elxp5  4752  fniinfv  5174  1stval2  5724  2ndval2  5725  fundmen  6222  xpsnen  6231
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