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Theorem sseq12i 3297
 Description: An equality inference for the subclass relationship. (Contributed by NM, 31-May-1999.) (Proof shortened by Eric Schmidt, 26-Jan-2007.)
Hypotheses
Ref Expression
sseq1i.1
sseq12i.2
Assertion
Ref Expression
sseq12i

Proof of Theorem sseq12i
StepHypRef Expression
1 sseq1i.1 . 2
2 sseq12i.2 . 2
3 sseq12 3294 . 2
41, 2, 3mp2an 653 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wceq 1642   wss 3257 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  df-ss 3259 This theorem is referenced by:  3sstr3i  3309  3sstr4i  3310  3sstr3g  3311  3sstr4g  3312  ss2rab  3342
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