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Theorem altopeq2 25523
Description: Equality for alternate ordered pairs. (Contributed by Scott Fenton, 22-Mar-2012.)
Assertion
Ref Expression
altopeq2  |-  ( A  =  B  ->  << C ,  A >>  =  << C ,  B >> )

Proof of Theorem altopeq2
StepHypRef Expression
1 eqid 2387 . 2  |-  C  =  C
2 altopeq12 25521 . 2  |-  ( ( C  =  C  /\  A  =  B )  -> 
<< C ,  A >>  = 
<< C ,  B >> )
31, 2mpan 652 1  |-  ( A  =  B  ->  << C ,  A >>  =  << C ,  B >> )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649   <<caltop 25515
This theorem is referenced by:  sbcaltop  25540
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368  ax-sep 4271  ax-nul 4279  ax-pr 4344
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-ne 2552  df-v 2901  df-dif 3266  df-un 3268  df-in 3270  df-ss 3277  df-nul 3572  df-sn 3763  df-pr 3764  df-altop 25517
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