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Theorem cmpcov2 20482
 Description: Rewrite cmpcov 20481 for the cover . (Contributed by Mario Carneiro, 11-Sep-2015.)
Hypothesis
Ref Expression
iscmp.1
Assertion
Ref Expression
cmpcov2
Distinct variable groups:   ,,,   ,,   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem cmpcov2
StepHypRef Expression
1 dfss3 3408 . . . . 5
2 elunirab 4202 . . . . . 6
32ralbii 2823 . . . . 5
41, 3sylbbr 219 . . . 4
5 ssrab2 3500 . . . . . . 7
65unissi 4213 . . . . . 6
7 iscmp.1 . . . . . 6
86, 7sseqtr4i 3451 . . . . 5
98a1i 11 . . . 4
104, 9eqssd 3435 . . 3
117cmpcov 20481 . . . 4
125, 11mp3an2 1378 . . 3
1310, 12sylan2 482 . 2
14 ssrab 3493 . . . . . . . 8
1514anbi1i 709 . . . . . . 7
16 an32 815 . . . . . . . 8
17 anass 661 . . . . . . . 8
1816, 17bitri 257 . . . . . . 7
1915, 18bitri 257 . . . . . 6
2019anbi1i 709 . . . . 5
21 an32 815 . . . . 5
22 an32 815 . . . . 5
2320, 21, 223bitr4i 285 . . . 4
24 elfpw 7894 . . . . 5
2524anbi1i 709 . . . 4
26 elfpw 7894 . . . . 5
2726anbi1i 709 . . . 4
2823, 25, 273bitr4i 285 . . 3
2928rexbii2 2879 . 2
3013, 29sylib 201 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 376   wceq 1452   wcel 1904  wral 2756  wrex 2757  crab 2760   cin 3389   wss 3390  cpw 3942  cuni 4190  cfn 7587  ccmp 20478 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-in 3397  df-ss 3404  df-pw 3944  df-uni 4191  df-cmp 20479 This theorem is referenced by:  cmpcovf  20483  bwth  20502  locfincmp  20618
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