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Theorem axcontlem1 25895
 Description: Lemma for axcont 25907. Change bound variables for later use. (Contributed by Scott Fenton, 20-Jun-2013.)
Hypothesis
Ref Expression
axcontlem1.1
Assertion
Ref Expression
axcontlem1
Distinct variable groups:   ,,,,   ,,,,,,   ,,,,,,   ,,,,,,
Allowed substitution hints:   (,)   (,,,,,)

Proof of Theorem axcontlem1
StepHypRef Expression
1 axcontlem1.1 . 2
2 eleq1 2495 . . . . 5
32adantr 452 . . . 4
4 eleq1 2495 . . . . . 6
54adantl 453 . . . . 5
6 fveq1 5719 . . . . . . . 8
7 oveq2 6081 . . . . . . . . . 10
87oveq1d 6088 . . . . . . . . 9
9 oveq1 6080 . . . . . . . . 9
108, 9oveq12d 6091 . . . . . . . 8
116, 10eqeqan12d 2450 . . . . . . 7
1211ralbidv 2717 . . . . . 6
13 fveq2 5720 . . . . . . . 8
14 fveq2 5720 . . . . . . . . . 10
1514oveq2d 6089 . . . . . . . . 9
16 fveq2 5720 . . . . . . . . . 10
1716oveq2d 6089 . . . . . . . . 9
1815, 17oveq12d 6091 . . . . . . . 8
1913, 18eqeq12d 2449 . . . . . . 7
2019cbvralv 2924 . . . . . 6
2112, 20syl6bb 253 . . . . 5
225, 21anbi12d 692 . . . 4
233, 22anbi12d 692 . . 3
2423cbvopabv 4269 . 2
251, 24eqtri 2455 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wceq 1652   wcel 1725  wral 2697  copab 4257  cfv 5446  (class class class)co 6073  cc0 8982  c1 8983   caddc 8985   cmul 8987   cpnf 9109   cmin 9283  cico 10910  cfz 11035 This theorem is referenced by:  axcontlem6  25900  axcontlem11  25905 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 2416 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-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-iota 5410  df-fv 5454  df-ov 6076
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