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Theorem ltordlem 9545
 Description: Lemma for ltord1 9546. (Contributed by Mario Carneiro, 14-Jun-2014.)
Hypotheses
Ref Expression
ltord.1
ltord.2
ltord.3
ltord.4
ltord.5
ltord.6
Assertion
Ref Expression
ltordlem
Distinct variable groups:   ,   ,,   ,,   ,,   ,,   ,,   ,,
Allowed substitution hints:   (,)   ()

Proof of Theorem ltordlem
StepHypRef Expression
1 ltord.6 . . 3
21ralrimivva 2791 . 2
3 breq1 4208 . . . 4
4 ltord.2 . . . . 5
54breq1d 4215 . . . 4
63, 5imbi12d 312 . . 3
7 breq2 4209 . . . 4
8 eqeq1 2442 . . . . . . 7
9 ltord.1 . . . . . . . 8
109eqeq1d 2444 . . . . . . 7
118, 10imbi12d 312 . . . . . 6
12 ltord.3 . . . . . 6
1311, 12chvarv 1969 . . . . 5
1413breq2d 4217 . . . 4
157, 14imbi12d 312 . . 3
166, 15rspc2v 3051 . 2
172, 16mpan9 456 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  wral 2698   wss 3313   class class class wbr 4205  cr 8982   clt 9113 This theorem is referenced by:  ltord1  9546 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-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2703  df-rab 2707  df-v 2951  df-dif 3316  df-un 3318  df-in 3320  df-ss 3327  df-nul 3622  df-if 3733  df-sn 3813  df-pr 3814  df-op 3816  df-br 4206
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