Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  reuxfr2d Structured version   Unicode version

Theorem reuxfr2d 4645
 Description: Transfer existential uniqueness from a variable to another variable contained in expression . (Contributed by NM, 16-Jan-2012.) (Revised by NM, 16-Jun-2017.)
Hypotheses
Ref Expression
reuxfr2d.1
reuxfr2d.2
Assertion
Ref Expression
reuxfr2d
Distinct variable groups:   ,,   ,   ,   ,,
Allowed substitution hints:   ()   ()

Proof of Theorem reuxfr2d
StepHypRef Expression
1 reuxfr2d.2 . . . . . . 7
2 rmoan 3276 . . . . . . 7
31, 2syl 17 . . . . . 6
4 ancom 451 . . . . . . 7
54rmobii 3027 . . . . . 6
63, 5sylib 199 . . . . 5
76ralrimiva 2846 . . . 4
8 2reuswap 3280 . . . 4
97, 8syl 17 . . 3
10 df-rmo 2790 . . . . . 6
1110ralbii 2863 . . . . 5
12 2reuswap 3280 . . . . 5
1311, 12sylbir 216 . . . 4
14 moeq 3253 . . . . . . 7
1514moani 2324 . . . . . 6
16 ancom 451 . . . . . . . 8
17 an12 804 . . . . . . . 8
1816, 17bitri 252 . . . . . . 7
1918mobii 2291 . . . . . 6
2015, 19mpbi 211 . . . . 5
2120a1i 11 . . . 4
2213, 21mprg 2795 . . 3
239, 22impbid1 206 . 2
24 reuxfr2d.1 . . . 4
25 biidd 240 . . . . 5
2625ceqsrexv 3211 . . . 4
2724, 26syl 17 . . 3
2827reubidva 3019 . 2
2923, 28bitrd 256 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   wceq 1437   wcel 1870  wmo 2267  wral 2782  wrex 2783  wreu 2784  wrmo 2785 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-eu 2270  df-mo 2271  df-clab 2415  df-cleq 2421  df-clel 2424  df-ral 2787  df-rex 2788  df-reu 2789  df-rmo 2790  df-v 3089 This theorem is referenced by:  reuxfr2  4646  reuxfrd  4647
 Copyright terms: Public domain W3C validator