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Theorem altopeq1 24497
Description: Equality for alternate ordered pairs. (Contributed by Scott Fenton, 22-Mar-2012.)
Assertion
Ref Expression
altopeq1  |-  ( A  =  B  ->  << A ,  C >>  =  << B ,  C >> )

Proof of Theorem altopeq1
StepHypRef Expression
1 eqid 2283 . 2  |-  C  =  C
2 altopeq12 24496 . 2  |-  ( ( A  =  B  /\  C  =  C )  -> 
<< A ,  C >>  = 
<< B ,  C >> )
31, 2mpan2 652 1  |-  ( A  =  B  ->  << A ,  C >>  =  << B ,  C >> )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623   <<caltop 24490
This theorem is referenced by:  sbcaltop  24515
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-sn 3646  df-pr 3647  df-altop 24492
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