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Theorem riota2df 6278
Description: A deduction version of riota2f 6279. (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:   ,

Proof of Theorem riota2df
StepHypRef Expression
1 riota2df.4 . . . 4
21adantr 465 . . 3
3 simpr 461 . . . 4
4 df-reu 2814 . . . 4
53, 4sylib 196 . . 3
6 simpr 461 . . . . . 6
72adantr 465 . . . . . 6
86, 7eqeltrd 2545 . . . . 5
98biantrurd 508 . . . 4
10 riota2df.5 . . . . 5
1110adantlr 714 . . . 4
129, 11bitr3d 255 . . 3
13 riota2df.1 . . . 4
14 nfreu1 3028 . . . 4
1513, 14nfan 1928 . . 3
16 riota2df.3 . . . 4
1716adantr 465 . . 3
18 riota2df.2 . . . 4
1918adantr 465 . . 3
202, 5, 12, 15, 17, 19iota2df 5580 . 2
21 df-riota 6257 . . 3
2221eqeq1i 2464 . 2
2320, 22syl6bbr 263 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  F/wnf 1616  e.wcel 1818  E!weu 2282  F/_wnfc 2605  E!wreu 2809  iotacio 5554  iota_crio 6256
This theorem is referenced by:  riota2f  6279  riota5f  6282  mapdheq  37455  hdmap1eq  37529  hdmapval2lem  37561
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-reu 2814  df-v 3111  df-sbc 3328  df-un 3480  df-sn 4030  df-pr 4032  df-uni 4250  df-iota 5556  df-riota 6257
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