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Theorem pmltpclem1 18640
 Description: Lemma for pmltpc 18642. (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 3923 . . . 4
8 fveq2 5377 . . . . . . 7
98breq1d 3930 . . . . . 6
109anbi1d 688 . . . . 5
118breq2d 3932 . . . . . 6
1211anbi1d 688 . . . . 5
1310, 12orbi12d 693 . . . 4
147, 133anbi13d 1259 . . 3
15 breq2 3924 . . . 4
16 breq1 3923 . . . 4
17 fveq2 5377 . . . . . . 7
1817breq2d 3932 . . . . . 6
1917breq2d 3932 . . . . . 6
2018, 19anbi12d 694 . . . . 5
2117breq1d 3930 . . . . . 6
2217breq1d 3930 . . . . . 6
2321, 22anbi12d 694 . . . . 5
2420, 23orbi12d 693 . . . 4
2515, 16, 243anbi123d 1257 . . 3
26 breq2 3924 . . . 4
27 fveq2 5377 . . . . . . 7
2827breq1d 3930 . . . . . 6
2928anbi2d 687 . . . . 5
3027breq2d 3932 . . . . . 6
3130anbi2d 687 . . . . 5
3229, 31orbi12d 693 . . . 4
3326, 323anbi23d 1260 . . 3
3414, 25, 33rcla43ev 2831 . 2
351, 2, 3, 4, 5, 6, 34syl33anc 1202 1
 Colors of variables: wff set class Syntax hints:   wi 6   wo 359   wa 360   w3a 939   wceq 1619   wcel 1621  wrex 2510   class class class wbr 3920  cfv 4592   clt 8747 This theorem is referenced by:  pmltpclem2  18641 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-rex 2514  df-rab 2516  df-v 2729  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553  df-uni 3728  df-br 3921  df-opab 3975  df-xp 4594  df-cnv 4596  df-dm 4598  df-rn 4599  df-res 4600  df-ima 4601  df-fv 4608
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