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Theorem riota2df 6231
 Description: A deduction version of riota2f 6232. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
riota2df.1
riota2df.2
riota2df.3
riota2df.4
riota2df.5
Assertion
Ref Expression
riota2df
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem riota2df
StepHypRef Expression
1 riota2df.4 . . . 4
3 simpr 462 . . . 4
4 df-reu 2721 . . . 4
53, 4sylib 199 . . 3
6 simpr 462 . . . . . 6
72adantr 466 . . . . . 6
86, 7eqeltrd 2506 . . . . 5
98biantrurd 510 . . . 4
10 riota2df.5 . . . . 5
1110adantlr 719 . . . 4
129, 11bitr3d 258 . . 3
13 riota2df.1 . . . 4
14 nfreu1 2938 . . . 4
1513, 14nfan 1988 . . 3
16 riota2df.3 . . . 4
18 riota2df.2 . . . 4
202, 5, 12, 15, 17, 19iota2df 5532 . 2
21 df-riota 6211 . . 3
2221eqeq1i 2433 . 2
2320, 22syl6bbr 266 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   wceq 1437  wnf 1661   wcel 1872  weu 2276  wnfc 2556  wreu 2716  cio 5506  crio 6210 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2063  ax-ext 2408 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-eu 2280  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2558  df-ral 2719  df-rex 2720  df-reu 2721  df-v 3024  df-sbc 3243  df-un 3384  df-sn 3942  df-pr 3944  df-uni 4163  df-iota 5508  df-riota 6211 This theorem is referenced by:  riota2f  6232  riota5f  6235  mapdheq  35208  hdmap1eq  35282  hdmapval2lem  35314
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