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

Theorem funsng 5298
 Description: A singleton of an ordered pair is a function. Theorem 10.5 of [Quine] p. 65. (Contributed by NM, 28-Jun-2011.)
Assertion
Ref Expression
funsng

Proof of Theorem funsng
StepHypRef Expression
1 funcnvsn 5297 . 2
2 cnvsng 5158 . . . 4
32ancoms 439 . . 3
43funeqd 5276 . 2
51, 4mpbii 202 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358   wceq 1623   wcel 1684  csn 3640  cop 3643  ccnv 4688   wfun 5249 This theorem is referenced by:  fnsng  5299  funsn  5300  funprg  5301  tfrlem10  6403  strle1  13239  bnj519  28764  bnj150  28908 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-id 4309  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-fun 5257
 Copyright terms: Public domain W3C validator