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Theorem riotaxfrd 6581
 Description: Change the variable in the expression for "the unique such that " to another variable contained in expression . Use reuhypd 4750 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:   ,   ,   ,,   ,,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem riotaxfrd
StepHypRef Expression
1 rabid 2884 . . . 4
21baib 872 . . 3
32riotabiia 6567 . 2
4 riotaxfrd.2 . . . . . 6
5 riotaxfrd.6 . . . . . 6
6 riotaxfrd.4 . . . . . 6
74, 5, 6reuxfrd 4748 . . . . 5
8 riotacl2 6563 . . . . . . . 8
98adantl 453 . . . . . . 7
10 riotacl 6564 . . . . . . . 8
11 nfriota1 6557 . . . . . . . . 9
12 riotaxfrd.1 . . . . . . . . 9
13 riotaxfrd.5 . . . . . . . . 9
1411, 12, 4, 6, 13rabxfrd 4744 . . . . . . . 8
1510, 14sylan2 461 . . . . . . 7
169, 15mpbird 224 . . . . . 6
1716ex 424 . . . . 5
187, 17sylbid 207 . . . 4
1918imp 419 . . 3
20 riotaxfrd.3 . . . . . . . 8
2120ex 424 . . . . . . 7
2210, 21syl5 30 . . . . . 6
237, 22sylbid 207 . . . . 5
2423imp 419 . . . 4
251baibr 873 . . . . . . 7
2625reubiia 2893 . . . . . 6
2726biimpi 187 . . . . 5
2827adantl 453 . . . 4
29 nfcv 2572 . . . . 5
30 nfrab1 2888 . . . . . 6
3130nfel2 2584 . . . . 5
32 eleq1 2496 . . . . 5
3329, 31, 32riota2f 6571 . . . 4
3424, 28, 33syl2anc 643 . . 3
3519, 34mpbid 202 . 2
363, 35syl5eqr 2482 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  wnfc 2559  wreu 2707  crab 2709  crio 6542 This theorem is referenced by:  riotaneg  9983  riotaocN  30007 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-reu 2712  df-rmo 2713  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-iota 5418  df-fv 5462  df-riota 6549
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