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Theorem nineq1i 3237
Description: Equality inference for anti-intersection. (Contributed by SF, 11-Jan-2015.)
Hypothesis
Ref Expression
nineqi.1 A = B
Assertion
Ref Expression
nineq1i (AC) = (BC)

Proof of Theorem nineq1i
StepHypRef Expression
1 nineqi.1 . 2 A = B
2 nineq1 3234 . 2 (A = B → (AC) = (BC))
31, 2ax-mp 5 1 (AC) = (BC)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1642  cnin 3204
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-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-nin 3211
This theorem is referenced by: (None)
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