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Theorem ordtypecbv 7486
 Description: Lemma for ordtype 7501. (Contributed by Mario Carneiro, 26-Jun-2015.)
Hypotheses
Ref Expression
ordtypelem.1 recs
ordtypelem.2
ordtypelem.3
Assertion
Ref Expression
ordtypecbv recs
Distinct variable groups:   ,,,,,   ,,,,,,,,,,   ,,,,,,,,
Allowed substitution hints:   (,)   (,,,,)   (,,,,,,,,,)   (,,,,,,,,,)

Proof of Theorem ordtypecbv
StepHypRef Expression
1 ordtypelem.1 . 2 recs
2 ordtypelem.3 . . . 4
3 breq1 4215 . . . . . . . . . 10
43notbid 286 . . . . . . . . 9
54cbvralv 2932 . . . . . . . 8
6 breq2 4216 . . . . . . . . . 10
76notbid 286 . . . . . . . . 9
87ralbidv 2725 . . . . . . . 8
95, 8syl5bb 249 . . . . . . 7
109cbvriotav 6561 . . . . . 6
11 ordtypelem.2 . . . . . . . . 9
12 breq1 4215 . . . . . . . . . . . 12
1312cbvralv 2932 . . . . . . . . . . 11
14 breq2 4216 . . . . . . . . . . . 12
1514ralbidv 2725 . . . . . . . . . . 11
1613, 15syl5bb 249 . . . . . . . . . 10
1716cbvrabv 2955 . . . . . . . . 9
1811, 17eqtri 2456 . . . . . . . 8
19 rneq 5095 . . . . . . . . . 10
2019raleqdv 2910 . . . . . . . . 9
2120rabbidv 2948 . . . . . . . 8
2218, 21syl5eq 2480 . . . . . . 7
2322raleqdv 2910 . . . . . . 7
2422, 23riotaeqbidv 6552 . . . . . 6
2510, 24syl5eq 2480 . . . . 5
2625cbvmptv 4300 . . . 4
272, 26eqtri 2456 . . 3
28 recseq 6634 . . 3 recs recs
2927, 28ax-mp 8 . 2 recs recs
301, 29eqtr2i 2457 1 recs
 Colors of variables: wff set class Syntax hints:   wn 3   wceq 1652  wral 2705  crab 2709  cvv 2956   class class class wbr 4212   cmpt 4266   crn 4879  crio 6542  recscrecs 6632 This theorem is referenced by:  oicl  7498  oif  7499  oiiso2  7500  ordtype  7501  oiiniseg  7502  ordtype2  7503 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-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-reu 2712  df-rab 2714  df-v 2958  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-opab 4267  df-mpt 4268  df-cnv 4886  df-dm 4888  df-rn 4889  df-iota 5418  df-fv 5462  df-riota 6549  df-recs 6633
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