Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  ackbij1lem1 Structured version   Unicode version

Theorem ackbij1lem1 8646
 Description: Lemma for ackbij2 8669. (Contributed by Stefan O'Rear, 18-Nov-2014.)
Assertion
Ref Expression
ackbij1lem1

Proof of Theorem ackbij1lem1
StepHypRef Expression
1 df-suc 5440 . . . 4
21ineq2i 3658 . . 3
3 indi 3716 . . 3
42, 3eqtri 2449 . 2
5 disjsn 4054 . . . . 5
65biimpri 209 . . . 4
76uneq2d 3617 . . 3
8 un0 3784 . . 3
97, 8syl6eq 2477 . 2
104, 9syl5eq 2473 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wceq 1437   wcel 1867   cun 3431   cin 3432  c0 3758  csn 3993   csuc 5436 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ral 2778  df-v 3080  df-dif 3436  df-un 3438  df-in 3440  df-nul 3759  df-sn 3994  df-suc 5440 This theorem is referenced by:  ackbij1lem15  8660  ackbij1lem16  8661
 Copyright terms: Public domain W3C validator