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Theorem phi011lem1 4598
 Description: Lemma for phi011 4599. (Contributed by SF, 3-Feb-2015.)
Assertion
Ref Expression
phi011lem1 Phi 0c Phi 0c Phi Phi

Proof of Theorem phi011lem1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssun1 3426 . . . . 5 Phi Phi 0c
21sseli 3269 . . . 4 Phi Phi 0c
3 eleq2 2414 . . . 4 Phi 0c Phi 0c Phi 0c Phi 0c
42, 3syl5ib 210 . . 3 Phi 0c Phi 0c Phi Phi 0c
5 0cnelphi 4597 . . . . . 6 0c Phi
6 eleq1 2413 . . . . . 6 0c Phi 0c Phi
75, 6mtbiri 294 . . . . 5 0c Phi
87con2i 112 . . . 4 Phi 0c
98a1i 10 . . 3 Phi 0c Phi 0c Phi 0c
10 elun 3220 . . . . . . 7 Phi 0c Phi 0c
11 df-sn 3741 . . . . . . . . 9 0c 0c
1211abeq2i 2460 . . . . . . . 8 0c 0c
1312orbi2i 505 . . . . . . 7 Phi 0c Phi 0c
1410, 13bitri 240 . . . . . 6 Phi 0c Phi 0c
1514biimpi 186 . . . . 5 Phi 0c Phi 0c
1615orcomd 377 . . . 4 Phi 0c 0c Phi
1716ord 366 . . 3 Phi 0c 0c Phi
184, 9, 17ee22 1362 . 2 Phi 0c Phi 0c Phi Phi
1918ssrdv 3278 1 Phi 0c Phi 0c Phi Phi
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wo 357   wceq 1642   wcel 1710   cun 3207   wss 3257  csn 3737  0cc0c 4374   Phi cphi 4562 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  ax-nin 4078  ax-sn 4087 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-ral 2619  df-rex 2620  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551  df-if 3663  df-sn 3741  df-int 3927  df-1c 4136  df-0c 4377  df-addc 4378  df-nnc 4379  df-phi 4565 This theorem is referenced by:  phi011  4599
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