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Theorem inteqd 3648
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 3646 . 2  |-  ( A  =  B  ->  |^| A  =  |^| B )
31, 2syl 14 1  |-  ( ph  ->  |^| A  =  |^| B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1259   |^|cint 3643
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-int 3644
This theorem is referenced by:  intprg  3676  op1stbg  4238  onsucmin  4261  elreldm  4588  elxp5  4837  fniinfv  5259  1stval2  5810  2ndval2  5811  fundmen  6317  xpsnen  6326  cardcl  6419  isnumi  6420  cardval3ex  6423  carden2bex  6427
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