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Theorem riotaxfrd 6288
Description: Change the variable in the expression for "the unique such that " to another variable contained in expression . Use reuhypd 4679 to eliminate the last hypothesis. (Contributed by NM, 16-Jan-2012.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
riotaxfrd.1
riotaxfrd.2
riotaxfrd.3
riotaxfrd.4
riotaxfrd.5
riotaxfrd.6
Assertion
Ref Expression
riotaxfrd
Distinct variable groups:   ,   ,   , ,   , ,   ,   ,

Proof of Theorem riotaxfrd
StepHypRef Expression
1 rabid 3034 . . . 4
21baib 903 . . 3
32riotabiia 6275 . 2
4 riotaxfrd.2 . . . . . 6
5 riotaxfrd.6 . . . . . 6
6 riotaxfrd.4 . . . . . 6
74, 5, 6reuxfrd 4677 . . . . 5
8 riotacl2 6271 . . . . . . . 8
98adantl 466 . . . . . . 7
10 riotacl 6272 . . . . . . . 8
11 nfriota1 6264 . . . . . . . . 9
12 riotaxfrd.1 . . . . . . . . 9
13 riotaxfrd.5 . . . . . . . . 9
1411, 12, 4, 6, 13rabxfrd 4673 . . . . . . . 8
1510, 14sylan2 474 . . . . . . 7
169, 15mpbird 232 . . . . . 6
1716ex 434 . . . . 5
187, 17sylbid 215 . . . 4
1918imp 429 . . 3
20 riotaxfrd.3 . . . . . . . 8
2120ex 434 . . . . . . 7
2210, 21syl5 32 . . . . . 6
237, 22sylbid 215 . . . . 5
2423imp 429 . . . 4
251baibr 904 . . . . . . 7
2625reubiia 3043 . . . . . 6
2726biimpi 194 . . . . 5
2827adantl 466 . . . 4
29 nfcv 2619 . . . . 5
30 nfrab1 3038 . . . . . 6
3130nfel2 2637 . . . . 5
32 eleq1 2529 . . . . 5
3329, 31, 32riota2f 6279 . . . 4
3424, 28, 33syl2anc 661 . . 3
3519, 34mpbid 210 . 2
363, 35syl5eqr 2512 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  F/_wnfc 2605  E!wreu 2809  {crab 2811  iota_crio 6256
This theorem is referenced by:  riotaneg  10543  zriotaneg  11002  riotaocN  34934
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-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-reu 2814  df-rmo 2815  df-rab 2816  df-v 3111  df-sbc 3328  df-un 3480  df-in 3482  df-ss 3489  df-sn 4030  df-pr 4032  df-uni 4250  df-iota 5556  df-riota 6257
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