Theorem seeq1 4856

Description: Equality theorem for the set-like predicate. (Contributed by Mario Carneiro, 24-Jun-2015.)

Assertion

Ref	Expression
seeq1

Proof of Theorem seeq1

Step	Hyp	Ref	Expression
1		eqimss2 3556	. . 3
2		sess1 4852	. . 3
3	1, 2	syl 16	. 2
4		eqimss 3555	. . 3
5		sess1 4852	. . 3
6	4, 5	syl 16	. 2
7	3, 6	impbid 191	1

Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  C_wss 3475  Sewse 4841

This theorem is referenced by:  oieq1  7958

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  ax-sep 4573

This theorem depends on definitions:  df-bi 185  df-or 370  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-in 3482  df-ss 3489  df-br 4453  df-se 4844