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Theorem compsscnvlem 8251
 Description: Lemma for compsscnv 8252. (Contributed by Mario Carneiro, 17-May-2015.)
Assertion
Ref Expression
compsscnvlem
Distinct variable group:   ,,

Proof of Theorem compsscnvlem
StepHypRef Expression
1 simpr 449 . . . 4
2 difss 3475 . . . 4
31, 2syl6eqss 3399 . . 3
4 vex 2960 . . . 4
54elpw 3806 . . 3
63, 5sylibr 205 . 2
71difeq2d 3466 . . 3
8 elpwi 3808 . . . . 5
98adantr 453 . . . 4
10 dfss4 3576 . . . 4
119, 10sylib 190 . . 3
127, 11eqtr2d 2470 . 2
136, 12jca 520 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726   cdif 3318   wss 3321  cpw 3800 This theorem is referenced by:  compsscnv  8252 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ral 2711  df-rab 2715  df-v 2959  df-dif 3324  df-in 3328  df-ss 3335  df-pw 3802
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