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Theorem cmpcov2 17173
 Description: Rewrite cmpcov 17172 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 3204 . . . . . 6
2 elunirab 3877 . . . . . . 7
32ralbii 2601 . . . . . 6
41, 3bitri 240 . . . . 5
54biimpri 197 . . . 4
6 ssrab2 3292 . . . . . . 7
7 uniss 3885 . . . . . . 7
86, 7ax-mp 8 . . . . . 6
9 iscmp.1 . . . . . 6
108, 9sseqtr4i 3245 . . . . 5
1110a1i 10 . . . 4
125, 11eqssd 3230 . . 3
139cmpcov 17172 . . . 4
146, 13mp3an2 1265 . . 3
1512, 14sylan2 460 . 2
16 ssrab 3285 . . . . . . . 8
1716anbi1i 676 . . . . . . 7
18 an32 773 . . . . . . . 8
19 anass 630 . . . . . . . 8
2018, 19bitri 240 . . . . . . 7
2117, 20bitri 240 . . . . . 6
2221anbi1i 676 . . . . 5
23 an32 773 . . . . 5
24 an32 773 . . . . 5
2522, 23, 243bitr4i 268 . . . 4
26 elfpw 7202 . . . . 5
2726anbi1i 676 . . . 4
28 elfpw 7202 . . . . 5
2928anbi1i 676 . . . 4
3025, 27, 293bitr4i 268 . . 3
3130rexbii2 2606 . 2
3215, 31sylib 188 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358   wceq 1633   wcel 1701  wral 2577  wrex 2578  crab 2581   cin 3185   wss 3186  cpw 3659  cuni 3864  cfn 6906  ccmp 17169 This theorem is referenced by:  cmpcovf  17174  locfincmp  25453 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297  ax-sep 4178 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-ral 2582  df-rex 2583  df-rab 2586  df-v 2824  df-in 3193  df-ss 3200  df-pw 3661  df-uni 3865  df-cmp 17170
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