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Theorem ineq1d 3456
 Description: Equality deduction for intersection of two classes. (Contributed by NM, 10-Apr-1994.)
Hypothesis
Ref Expression
ineq1d.1 (φA = B)
Assertion
Ref Expression
ineq1d (φ → (AC) = (BC))

Proof of Theorem ineq1d
StepHypRef Expression
1 ineq1d.1 . 2 (φA = B)
2 ineq1 3450 . 2 (A = B → (AC) = (BC))
31, 2syl 15 1 (φ → (AC) = (BC))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642   ∩ cin 3208 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-or 359  df-an 360  df-nan 1288  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-v 2861  df-nin 3211  df-compl 3212  df-in 3213 This theorem is referenced by:  diftpsn3  3849  iinrab2  4029  pw1eq  4143  cokeq1  4230  nndisjeq  4429  fnresdisj  5193  fnimadisj  5203  txpeq1  5779
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