Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  compsscnvlem Unicode version

Theorem compsscnvlem 8012
 Description: Lemma for compsscnv 8013. (Contributed by Mario Carneiro, 17-May-2015.)
Assertion
Ref Expression
compsscnvlem
Distinct variable group:   ,,

Proof of Theorem compsscnvlem
StepHypRef Expression
1 difss 3316 . . . 4
2 simpr 447 . . . . 5
32sseq1d 3218 . . . 4
41, 3mpbiri 224 . . 3
5 vex 2804 . . . 4
65elpw 3644 . . 3
74, 6sylibr 203 . 2
82difeq2d 3307 . . 3
9 elpwi 3646 . . . . 5
109adantr 451 . . . 4
11 dfss4 3416 . . . 4
1210, 11sylib 188 . . 3
138, 12eqtr2d 2329 . 2
147, 13jca 518 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358   wceq 1632   wcel 1696   cdif 3162   wss 3165  cpw 3638 This theorem is referenced by:  compsscnv  8013 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rab 2565  df-v 2803  df-dif 3168  df-in 3172  df-ss 3179  df-pw 3640
 Copyright terms: Public domain W3C validator