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Theorem riota2df 6341
 Description: A deduction version of riota2f 6342. (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
21adantr 451 . . 3
3 simpr 447 . . . 4
4 df-reu 2563 . . . 4
53, 4sylib 188 . . 3
6 simpr 447 . . . . . 6
72adantr 451 . . . . . 6
86, 7eqeltrd 2370 . . . . 5
98biantrurd 494 . . . 4
10 riota2df.5 . . . . 5
1110adantlr 695 . . . 4
129, 11bitr3d 246 . . 3
13 riota2df.1 . . . 4
14 nfreu1 2723 . . . 4
1513, 14nfan 1783 . . 3
16 riota2df.3 . . . 4
1716adantr 451 . . 3
18 riota2df.2 . . . 4
1918adantr 451 . . 3
202, 5, 12, 15, 17, 19iota2df 5259 . 2
21 riotaiota 6326 . . . 4
2221adantl 452 . . 3
2322eqeq1d 2304 . 2
2420, 23bitr4d 247 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wnf 1534   wceq 1632   wcel 1696  weu 2156  wnfc 2419  wreu 2558  cio 5233  crio 6313 This theorem is referenced by:  riota2f  6342  riota5f  6345  riotasvdOLD  6364  cdlemk36  31724  mapdheq  32540  hdmap1eq  32614  hdmapval2lem  32646 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-reu 2563  df-v 2803  df-sbc 3005  df-un 3170  df-if 3579  df-sn 3659  df-pr 3660  df-uni 3844  df-iota 5235  df-riota 6320
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