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Theorem ssn0 3583
Description: A class with a nonempty subclass is nonempty. (Contributed by NM, 17-Feb-2007.)
Assertion
Ref Expression
ssn0 ((A B A) → B)

Proof of Theorem ssn0
StepHypRef Expression
1 sseq0 3582 . . . 4 ((A B B = ) → A = )
21ex 423 . . 3 (A B → (B = A = ))
32necon3d 2554 . 2 (A B → (AB))
43imp 418 1 ((A B A) → B)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358   = wceq 1642  wne 2516   wss 3257  c0 3550
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-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-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-ss 3259  df-nul 3551
This theorem is referenced by: (None)
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