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Theorem pmltpclem1 19298
 Description: Lemma for pmltpc 19300. (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 4175 . . . 4
8 fveq2 5687 . . . . . . 7
98breq1d 4182 . . . . . 6
109anbi1d 686 . . . . 5
118breq2d 4184 . . . . . 6
1211anbi1d 686 . . . . 5
1310, 12orbi12d 691 . . . 4
147, 133anbi13d 1256 . . 3
15 breq2 4176 . . . 4
16 breq1 4175 . . . 4
17 fveq2 5687 . . . . . . 7
1817breq2d 4184 . . . . . 6
1917breq2d 4184 . . . . . 6
2018, 19anbi12d 692 . . . . 5
2117breq1d 4182 . . . . . 6
2217breq1d 4182 . . . . . 6
2321, 22anbi12d 692 . . . . 5
2420, 23orbi12d 691 . . . 4
2515, 16, 243anbi123d 1254 . . 3
26 breq2 4176 . . . 4
27 fveq2 5687 . . . . . . 7
2827breq1d 4182 . . . . . 6
2928anbi2d 685 . . . . 5
3027breq2d 4184 . . . . . 6
3130anbi2d 685 . . . . 5
3229, 31orbi12d 691 . . . 4
3326, 323anbi23d 1257 . . 3
3414, 25, 33rspc3ev 3022 . 2
351, 2, 3, 4, 5, 6, 34syl33anc 1199 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 358   wa 359   w3a 936   wceq 1649   wcel 1721  wrex 2667   class class class wbr 4172  cfv 5413   clt 9076 This theorem is referenced by:  pmltpclem2  19299 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-rex 2672  df-rab 2675  df-v 2918  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-uni 3976  df-br 4173  df-iota 5377  df-fv 5421
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