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Theorem indif1 3577
 Description: Bring an intersection in and out of a class difference. (Contributed by Mario Carneiro, 15-May-2015.)
Assertion
Ref Expression
indif1

Proof of Theorem indif1
StepHypRef Expression
1 indif2 3576 . 2
2 incom 3525 . 2
3 incom 3525 . . 3
43difeq1i 3453 . 2
51, 2, 43eqtr3i 2463 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   cdif 3309   cin 3311 This theorem is referenced by:  hartogslem1  7503  fpwwe2  8510  leiso  11700  basdif0  17010  tgdif0  17049  kqdisj  17756  trufil  17934  gtiso  24080  dfon4  25730 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rab 2706  df-v 2950  df-dif 3315  df-in 3319
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