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Theorem altopeq2 25814
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 2438 . 2  |-  C  =  C
2 altopeq12 25812 . 2  |-  ( ( C  =  C  /\  A  =  B )  -> 
<< C ,  A >>  = 
<< C ,  B >> )
31, 2mpan 653 1  |-  ( A  =  B  ->  << C ,  A >>  =  << C ,  B >> )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1653   <<caltop 25806
This theorem is referenced by:  sbcaltop  25831
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-sn 3822  df-pr 3823  df-altop 25808
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