ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  reusv1 Structured version   Unicode version

Theorem reusv1 4156
Description: Two ways to express single-valuedness of a class expression  C. (Contributed by NM, 16-Dec-2012.) (Proof shortened by Mario Carneiro, 18-Nov-2016.)
Assertion
Ref Expression
reusv1  C  C
Distinct variable groups:   ,   ,   , C   ,   ,
Allowed substitution hints:   ()   ()   ()    C()

Proof of Theorem reusv1
StepHypRef Expression
1 nfra1 2349 . . . 4  F/  C
21nfmo 1917 . . 3  F/  C
3 rsp 2363 . . . . . . . 8  C  C
43impd 242 . . . . . . 7  C  C
54com12 27 . . . . . 6  C  C
65alrimiv 1751 . . . . 5  C  C
7 moeq 2710 . . . . 5  C
8 moim 1961 . . . . 5  C  C  C  C
96, 7, 8mpisyl 1332 . . . 4  C
109ex 108 . . 3  C
112, 10rexlimi 2420 . 2  C
12 mormo 2515 . 2  C  C
13 reu5 2516 . . 3  C  C  C
1413rbaib 829 . 2  C  C  C
1511, 12, 143syl 17 1  C  C
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240   wceq 1242   wcel 1390  wmo 1898  wral 2300  wrex 2301  wreu 2302  wrmo 2303
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-ral 2305  df-rex 2306  df-reu 2307  df-rmo 2308  df-v 2553
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator