Mathbox for Thierry Arnoux < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  elabreximd Unicode version

Theorem elabreximd 23055
 Description: Class substitution in an image set. (Contributed by Thierry Arnoux, 30-Dec-2016.)
Hypotheses
Ref Expression
elabreximd.1
elabreximd.2
elabreximd.3
elabreximd.4
elabreximd.5
Assertion
Ref Expression
elabreximd
Distinct variable groups:   ,,   ,   ,
Allowed substitution hints:   (,)   (,)   (,)   ()   ()   (,)

Proof of Theorem elabreximd
StepHypRef Expression
1 elabreximd.4 . . . . 5
2 nfv 1609 . . . . . . 7
3 eqeq1 2302 . . . . . . 7
42, 3rexbid 2575 . . . . . 6
54elabg 2928 . . . . 5
61, 5syl 15 . . . 4
76biimpd 198 . . 3
87imp 418 . 2
9 elabreximd.1 . . . 4
10 elabreximd.2 . . . 4
11 simpr 447 . . . . . 6
12 elabreximd.5 . . . . . . 7
1312adantr 451 . . . . . 6
14 elabreximd.3 . . . . . . 7
1514biimpar 471 . . . . . 6
1611, 13, 15syl2anc 642 . . . . 5
1716exp31 587 . . . 4
189, 10, 17rexlimd 2677 . . 3
1918imp 418 . 2
208, 19syldan 456 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wnf 1534   wceq 1632   wcel 1696  cab 2282  wrex 2557 This theorem is referenced by:  abrexss  23056  elabreximdv  23208  disjabrex  23374  disjabrexf  23375 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-rex 2562  df-v 2803
 Copyright terms: Public domain W3C validator