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Theorem inteqd 3931
 Description: Equality deduction for class intersection. (Contributed by NM, 2-Sep-2003.)
Hypothesis
Ref Expression
inteqd.1 (φA = B)
Assertion
Ref Expression
inteqd (φA = B)

Proof of Theorem inteqd
StepHypRef Expression
1 inteqd.1 . 2 (φA = B)
2 inteq 3929 . 2 (A = BA = B)
31, 2syl 15 1 (φA = B)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642  ∩cint 3926 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-int 3927 This theorem is referenced by:  intprg  3960  fniinfv  5372
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