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Theorem inteqd 3620
Description: Equality deduction for class intersection. (Contributed by NM, 2-Sep-2003.)
Hypothesis
Ref Expression
inteqd.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
inteqd  |-  ( ph  ->  |^| A  =  |^| B )

Proof of Theorem inteqd
StepHypRef Expression
1 inteqd.1 . 2  |-  ( ph  ->  A  =  B )
2 inteq 3618 . 2  |-  ( A  =  B  ->  |^| A  =  |^| B )
31, 2syl 14 1  |-  ( ph  ->  |^| A  =  |^| B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1243   |^|cint 3615
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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-int 3616
This theorem is referenced by:  intprg  3648  op1stbg  4210  onsucmin  4233  elreldm  4560  elxp5  4809  fniinfv  5231  1stval2  5782  2ndval2  5783  fundmen  6286  xpsnen  6295  cardcl  6361  isnumi  6362  cardval3ex  6365  carden2bex  6369
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