Mathbox for Scott Fenton < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  altopthc Structured version   Unicode version

Theorem altopthc 25808
 Description: Alternate ordered pair theorem with different sethood requirements. See altopth 25806 for more comments. (Contributed by Scott Fenton, 14-Apr-2012.)
Hypotheses
Ref Expression
altopthc.1
altopthc.2
Assertion
Ref Expression
altopthc

Proof of Theorem altopthc
StepHypRef Expression
1 eqcom 2437 . 2
2 altopthc.2 . . 3
3 altopthc.1 . . 3
42, 3altopthb 25807 . 2
5 eqcom 2437 . . 3
6 eqcom 2437 . . 3
75, 6anbi12i 679 . 2
81, 4, 73bitri 263 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wceq 1652   wcel 1725  cvv 2948  caltop 25793 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-sn 3812  df-pr 3813  df-altop 25795
 Copyright terms: Public domain W3C validator