MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  fin1ai Unicode version

Theorem fin1ai 8694
Description: Property of a Ia-finite set. (Contributed by Stefan O'Rear, 16-May-2015.)
Assertion
Ref Expression
fin1ai

Proof of Theorem fin1ai
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elpw2g 4615 . . 3
21biimpar 485 . 2
3 isfin1a 8693 . . . 4
43ibi 241 . . 3
54adantr 465 . 2
6 eleq1 2529 . . . 4
7 difeq2 3615 . . . . 5
87eleq1d 2526 . . . 4
96, 8orbi12d 709 . . 3
109rspcv 3206 . 2
112, 5, 10sylc 60 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  \/wo 368  /\wa 369  =wceq 1395  e.wcel 1818  A.wral 2807  \cdif 3472  C_wss 3475  ~Pcpw 4012   cfn 7536   cfin1a 8679
This theorem is referenced by:  enfin1ai  8785  fin1a2  8816  fin1aufil  20433
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-pw 4014  df-fin1a 8686
  Copyright terms: Public domain W3C validator