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Theorem altopeq2 24570
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 2296 . 2  |-  C  =  C
2 altopeq12 24568 . 2  |-  ( ( C  =  C  /\  A  =  B )  -> 
<< C ,  A >>  = 
<< C ,  B >> )
31, 2mpan 651 1  |-  ( A  =  B  ->  << C ,  A >>  =  << C ,  B >> )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1632   <<caltop 24562
This theorem is referenced by:  sbcaltop  24587
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-sn 3659  df-pr 3660  df-altop 24564
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