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Theorem onovuni 6596
 Description: A variant of onfununi 6595 for operations. (Contributed by Eric Schmidt, 26-May-2009.) (Revised by Mario Carneiro, 11-Sep-2015.)
Hypotheses
Ref Expression
onovuni.1
onovuni.2
Assertion
Ref Expression
onovuni
Distinct variable groups:   ,,   ,,   ,,   ,
Allowed substitution hint:   ()

Proof of Theorem onovuni
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 onovuni.1 . . . 4
2 vex 2951 . . . . 5
3 oveq2 6081 . . . . . 6
4 eqid 2435 . . . . . 6
5 ovex 6098 . . . . . 6
63, 4, 5fvmpt 5798 . . . . 5
72, 6ax-mp 8 . . . 4
8 vex 2951 . . . . . . 7
9 oveq2 6081 . . . . . . . 8
10 ovex 6098 . . . . . . . 8
119, 4, 10fvmpt 5798 . . . . . . 7
128, 11ax-mp 8 . . . . . 6
1312a1i 11 . . . . 5
1413iuneq2i 4103 . . . 4
151, 7, 143eqtr4g 2492 . . 3
16 onovuni.2 . . . 4
1716, 12, 73sstr4g 3381 . . 3
1815, 17onfununi 6595 . 2
19 uniexg 4698 . . . 4
20 oveq2 6081 . . . . 5
21 ovex 6098 . . . . 5
2220, 4, 21fvmpt 5798 . . . 4
2319, 22syl 16 . . 3
2512a1i 11 . . . 4
2625iuneq2i 4103 . . 3
2726a1i 11 . 2
2818, 24, 273eqtr3d 2475 1
 Colors of variables: wff set class Syntax hints:   wi 4   w3a 936   wceq 1652   wcel 1725   wne 2598  cvv 2948   wss 3312  c0 3620  cuni 4007  ciun 4085   cmpt 4258  con0 4573   wlim 4574  cfv 5446  (class class class)co 6073 This theorem is referenced by:  onoviun  6597 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395  ax-un 4693 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-pss 3328  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-tp 3814  df-op 3815  df-uni 4008  df-iun 4087  df-br 4205  df-opab 4259  df-mpt 4260  df-tr 4295  df-eprel 4486  df-id 4490  df-po 4495  df-so 4496  df-fr 4533  df-we 4535  df-ord 4576  df-on 4577  df-lim 4578  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-iota 5410  df-fun 5448  df-fv 5454  df-ov 6076
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