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Theorem tposeqd 6876
Description: Equality theorem for transposition. (Contributed by Mario Carneiro, 7-Jan-2017.)
Hypothesis
Ref Expression
tposeqd.1  |-  ( ph  ->  F  =  G )
Assertion
Ref Expression
tposeqd  |-  ( ph  -> tpos  F  = tpos  G )

Proof of Theorem tposeqd
StepHypRef Expression
1 tposeqd.1 . 2  |-  ( ph  ->  F  =  G )
2 tposeq 6875 . 2  |-  ( F  =  G  -> tpos  F  = tpos 
G )
31, 2syl 16 1  |-  ( ph  -> tpos  F  = tpos  G )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1399  tpos ctpos 6872
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1626  ax-4 1639  ax-5 1712  ax-6 1755  ax-7 1798  ax-9 1830  ax-10 1845  ax-11 1850  ax-12 1862  ax-13 2006  ax-ext 2360  ax-sep 4488  ax-nul 4496  ax-pr 4601
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 973  df-tru 1402  df-ex 1621  df-nf 1625  df-sb 1748  df-clab 2368  df-cleq 2374  df-clel 2377  df-nfc 2532  df-ne 2579  df-ral 2737  df-rex 2738  df-rab 2741  df-v 3036  df-dif 3392  df-un 3394  df-in 3396  df-ss 3403  df-nul 3712  df-if 3858  df-sn 3945  df-pr 3947  df-op 3951  df-br 4368  df-opab 4426  df-mpt 4427  df-xp 4919  df-rel 4920  df-cnv 4921  df-co 4922  df-dm 4923  df-res 4925  df-tpos 6873
This theorem is referenced by:  oppcval  15119  oppchomfval  15120  oppccofval  15122  oppchomfpropd  15132  oppcmon  15144  oppgval  16499  oppgplusfval  16500  oppglsm  16779  opprval  17386  opprmulfval  17387  mattposvs  19042  mattpos1  19043  mamutpos  19045  mattposm  19046  madulid  19232
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