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Theorem ceexlem1 6194
Description: Lemma for ceex 6195. Set up part of the stratification. (Contributed by SF, 6-Mar-2015.)
Assertion
Ref Expression
ceexlem1 SSet SI Pw1Fn 1
Distinct variable group:   ,

Proof of Theorem ceexlem1
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 snex 4111 . . . . . . . 8
21brsnsi1 5805 . . . . . . 7 SI Pw1Fn Pw1Fn
32anbi1i 676 . . . . . 6 SI Pw1Fn SSet Pw1Fn SSet
4 19.41v 1901 . . . . . 6 Pw1Fn SSet Pw1Fn SSet
5 anass 630 . . . . . . 7 Pw1Fn SSet Pw1Fn SSet
65exbii 1582 . . . . . 6 Pw1Fn SSet Pw1Fn SSet
73, 4, 63bitr2i 264 . . . . 5 SI Pw1Fn SSet Pw1Fn SSet
87exbii 1582 . . . 4 SI Pw1Fn SSet Pw1Fn SSet
9 excom 1741 . . . 4 Pw1Fn SSet Pw1Fn SSet
108, 9bitri 240 . . 3 SI Pw1Fn SSet Pw1Fn SSet
11 snex 4111 . . . . . 6
12 breq1 4634 . . . . . . 7 SSet SSet
1312anbi2d 684 . . . . . 6 Pw1Fn SSet Pw1Fn SSet
1411, 13ceqsexv 2894 . . . . 5 Pw1Fn SSet Pw1Fn SSet
15 vex 2862 . . . . . . 7
1615brpw1fn 5880 . . . . . 6 Pw1Fn 1
17 vex 2862 . . . . . . 7
18 vex 2862 . . . . . . 7
1917, 18brssetsn 4751 . . . . . 6 SSet
2016, 19anbi12i 678 . . . . 5 Pw1Fn SSet 1
2114, 20bitri 240 . . . 4 Pw1Fn SSet 1
2221exbii 1582 . . 3 Pw1Fn SSet 1
2310, 22bitri 240 . 2 SI Pw1Fn SSet 1
24 opelco 4896 . 2 SSet SI Pw1Fn SI Pw1Fn SSet
25 df-clel 2349 . 2 1 1
2623, 24, 253bitr4i 268 1 SSet SI Pw1Fn 1
Colors of variables: wff set class
Syntax hints:   wb 176   wa 358  wex 1541   wceq 1642   wcel 1710  csn 3737  1 cpw1 4135  cop 4561   class class class wbr 4631   SSet csset 4711   SI csi 4712   ccom 4713   Pw1Fn cpw1fn 5785
This theorem is referenced by:  ceex  6195
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-13 1712  ax-14 1714  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334  ax-nin 4078  ax-xp 4079  ax-cnv 4080  ax-1c 4081  ax-sset 4082  ax-si 4083  ax-ins2 4084  ax-ins3 4085  ax-typlower 4086  ax-sn 4087
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-3an 936  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-ral 2619  df-rex 2620  df-reu 2621  df-rmo 2622  df-rab 2623  df-v 2861  df-sbc 3047  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-symdif 3216  df-ss 3259  df-pss 3261  df-nul 3551  df-if 3663  df-pw 3724  df-sn 3741  df-pr 3742  df-uni 3892  df-int 3927  df-opk 4058  df-1c 4136  df-pw1 4137  df-uni1 4138  df-xpk 4185  df-cnvk 4186  df-ins2k 4187  df-ins3k 4188  df-imak 4189  df-cok 4190  df-p6 4191  df-sik 4192  df-ssetk 4193  df-imagek 4194  df-idk 4195  df-iota 4339  df-0c 4377  df-addc 4378  df-nnc 4379  df-fin 4380  df-lefin 4439  df-ltfin 4440  df-ncfin 4441  df-tfin 4442  df-evenfin 4443  df-oddfin 4444  df-sfin 4445  df-spfin 4446  df-phi 4565  df-op 4566  df-proj1 4567  df-proj2 4568  df-opab 4615  df-br 4632  df-sset 4717  df-co 4718  df-ima 4719  df-si 4720  df-id 4759  df-xp 4777  df-rel 4778  df-cnv 4779  df-rn 4780  df-dm 4781  df-fun 4783  df-fn 4784  df-fv 4789  df-mpt 5693  df-pw1fn 5801
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