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

Theorem elabreximd 23984
 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 . . . 4
2 eqeq1 2442 . . . . . 6
32rexbidv 2719 . . . . 5
43elabg 3076 . . . 4
51, 4syl 16 . . 3
65biimpa 471 . 2
7 elabreximd.1 . . . 4
8 elabreximd.2 . . . 4
9 simpr 448 . . . . . 6
10 elabreximd.5 . . . . . . 7
1110adantr 452 . . . . . 6
12 elabreximd.3 . . . . . . 7
1312biimpar 472 . . . . . 6
149, 11, 13syl2anc 643 . . . . 5
1514exp31 588 . . . 4
167, 8, 15rexlimd 2820 . . 3
1716imp 419 . 2
186, 17syldan 457 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wnf 1553   wceq 1652   wcel 1725  cab 2422  wrex 2699 This theorem is referenced by:  elabreximdv  23985  abrexss  23986  disjabrex  24017  disjabrexf  24018 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2703  df-rex 2704  df-v 2951
 Copyright terms: Public domain W3C validator