Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  eqreu Unicode version

Theorem eqreu 2733
 Description: A condition which implies existential uniqueness. (Contributed by Mario Carneiro, 2-Oct-2015.)
Hypothesis
Ref Expression
eqreu.1
Assertion
Ref Expression
eqreu
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem eqreu
StepHypRef Expression
1 ralbiim 2447 . . . . 5
2 eqreu.1 . . . . . . 7
32ceqsralv 2585 . . . . . 6
43anbi2d 437 . . . . 5
51, 4syl5bb 181 . . . 4
6 reu6i 2732 . . . . 5
76ex 108 . . . 4
85, 7sylbird 159 . . 3
983impib 1102 . 2
1093com23 1110 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   w3a 885   wceq 1243   wcel 1393  wral 2306  wreu 2308 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-reu 2313  df-v 2559 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator