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Theorem bnj1416 33174
 Description: Technical lemma for bnj60 33197. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1416.1
bnj1416.2
bnj1416.3
bnj1416.4
bnj1416.5
bnj1416.6
bnj1416.7
bnj1416.8
bnj1416.9
bnj1416.10
bnj1416.11
bnj1416.12
bnj1416.28
Assertion
Ref Expression
bnj1416

Proof of Theorem bnj1416
StepHypRef Expression
1 bnj1416.12 . . . 4
21dmeqi 5202 . . 3
3 dmun 5207 . . 3
4 fvex 5874 . . . . 5
54dmsnop 5480 . . . 4
65uneq2i 3655 . . 3
72, 3, 63eqtri 2500 . 2
8 bnj1416.28 . . . 4
98uneq1d 3657 . . 3
10 uncom 3648 . . 3
119, 10syl6eq 2524 . 2
127, 11syl5eq 2520 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184   wa 369   w3a 973   wceq 1379  wex 1596   wcel 1767  cab 2452   wne 2662  wral 2814  wrex 2815  crab 2818  wsbc 3331   cun 3474   wss 3476  c0 3785  csn 4027  cop 4033  cuni 4245   class class class wbr 4447   cdm 4999   cres 5001   wfn 5581  cfv 5586   c-bnj14 32820   w-bnj15 32824   c-bnj18 32826 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pr 4686 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-sbc 3332  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-uni 4246  df-br 4448  df-dm 5009  df-iota 5549  df-fv 5594 This theorem is referenced by:  bnj1312  33193
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