Theorem indif1 3741

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

Step	Hyp	Ref	Expression
1		indif2 3740	. 2
2		incom 3690	. 2
3		incom 3690	. . 3
4	3	difeq1i 3617	. 2
5	1, 2, 4	3eqtr3i 2494	1

Syntax hints:  =wceq 1395  \cdif 3472  i^icin 3474

This theorem is referenced by:  resdmdfsn  5324  hartogslem1  7988  fpwwe2  9042  leiso  12508  basdif0  19454  tgdif0  19494  kqdisj  20233  trufil  20411  gtiso  27519  dfon4  29543

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-in 3482