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Theorem inteqd 3647
 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 3645 . 2 (𝐴 = 𝐵 𝐴 = 𝐵)
31, 2syl 14 1 (𝜑 𝐴 = 𝐵)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1259  ∩ cint 3642 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 3643 This theorem is referenced by:  intprg  3675  op1stbg  4237  onsucmin  4260  elreldm  4587  elxp5  4836  fniinfv  5258  1stval2  5809  2ndval2  5810  fundmen  6316  xpsnen  6325  cardcl  6418  isnumi  6419  cardval3ex  6422  carden2bex  6426
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