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Theorem pmltpclem1 19376
 Description: Lemma for pmltpc 19378. (Contributed by Mario Carneiro, 1-Jul-2014.)
Hypotheses
Ref Expression
pmltpclem1.1
pmltpclem1.2
pmltpclem1.3
pmltpclem1.4
pmltpclem1.5
pmltpclem1.6
Assertion
Ref Expression
pmltpclem1
Distinct variable groups:   ,,,   ,,   ,   ,,,   ,,,
Allowed substitution hints:   (,,)   ()   (,)

Proof of Theorem pmltpclem1
StepHypRef Expression
1 pmltpclem1.1 . 2
2 pmltpclem1.2 . 2
3 pmltpclem1.3 . 2
4 pmltpclem1.4 . 2
5 pmltpclem1.5 . 2
6 pmltpclem1.6 . 2
7 breq1 4240 . . . 4
8 fveq2 5757 . . . . . . 7
98breq1d 4247 . . . . . 6
109anbi1d 687 . . . . 5
118breq2d 4249 . . . . . 6
1211anbi1d 687 . . . . 5
1310, 12orbi12d 692 . . . 4
147, 133anbi13d 1257 . . 3
15 breq2 4241 . . . 4
16 breq1 4240 . . . 4
17 fveq2 5757 . . . . . . 7
1817breq2d 4249 . . . . . 6
1917breq2d 4249 . . . . . 6
2018, 19anbi12d 693 . . . . 5
2117breq1d 4247 . . . . . 6
2217breq1d 4247 . . . . . 6
2321, 22anbi12d 693 . . . . 5
2420, 23orbi12d 692 . . . 4
2515, 16, 243anbi123d 1255 . . 3
26 breq2 4241 . . . 4
27 fveq2 5757 . . . . . . 7
2827breq1d 4247 . . . . . 6
2928anbi2d 686 . . . . 5
3027breq2d 4249 . . . . . 6
3130anbi2d 686 . . . . 5
3229, 31orbi12d 692 . . . 4
3326, 323anbi23d 1258 . . 3
3414, 25, 33rspc3ev 3068 . 2
351, 2, 3, 4, 5, 6, 34syl33anc 1200 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 359   wa 360   w3a 937   wceq 1653   wcel 1727  wrex 2712   class class class wbr 4237  cfv 5483   clt 9151 This theorem is referenced by:  pmltpclem2  19377 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-rex 2717  df-rab 2720  df-v 2964  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-op 3847  df-uni 4040  df-br 4238  df-iota 5447  df-fv 5491
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