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Theorem altopthbg 28117
Description: Alternate ordered pair theorem. (Contributed by Scott Fenton, 14-Apr-2012.)
Assertion
Ref Expression
altopthbg

Proof of Theorem altopthbg
StepHypRef Expression
1 altopthsn 28110 . 2
2 sneqbg 4125 . . 3
3 sneqbg 4125 . . . 4
4 eqcom 2458 . . . 4
5 eqcom 2458 . . . 4
63, 4, 53bitr4g 288 . . 3
72, 6bi2anan9 868 . 2
81, 7syl5bb 257 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1370  e.wcel 1757  {csn 3959  <<caltop 28105
This theorem is referenced by:  altopthb  28119
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1709  ax-7 1729  ax-9 1761  ax-10 1776  ax-11 1781  ax-12 1793  ax-13 1944  ax-ext 2429  ax-sep 4495  ax-nul 4503  ax-pr 4613
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1702  df-clab 2436  df-cleq 2442  df-clel 2445  df-nfc 2598  df-ne 2643  df-v 3054  df-dif 3413  df-un 3415  df-in 3417  df-ss 3424  df-nul 3720  df-sn 3960  df-pr 3962  df-altop 28107
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