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Theorem iineq2dv 3991
 Description: Equality deduction for indexed intersection. (Contributed by NM, 3-Aug-2004.)
Hypothesis
Ref Expression
iuneq2dv.1 ((φ x A) → B = C)
Assertion
Ref Expression
iineq2dv (φx A B = x A C)
Distinct variable group:   φ,x
Allowed substitution hints:   A(x)   B(x)   C(x)

Proof of Theorem iineq2dv
StepHypRef Expression
1 nfv 1619 . 2 xφ
2 iuneq2dv.1 . 2 ((φ x A) → B = C)
31, 2iineq2d 3989 1 (φx A B = x A C)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   = wceq 1642   ∈ wcel 1710  ∩ciin 3970 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-ral 2619  df-iin 3972 This theorem is referenced by: (None)
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