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Theorem tposeqd 7520
Description: Equality theorem for transposition. (Contributed by Mario Carneiro, 7-Jan-2017.)
Hypothesis
Ref Expression
tposeqd.1 (𝜑𝐹 = 𝐺)
Assertion
Ref Expression
tposeqd (𝜑 → tpos 𝐹 = tpos 𝐺)

Proof of Theorem tposeqd
StepHypRef Expression
1 tposeqd.1 . 2 (𝜑𝐹 = 𝐺)
2 tposeq 7519 . 2 (𝐹 = 𝐺 → tpos 𝐹 = tpos 𝐺)
31, 2syl 17 1 (𝜑 → tpos 𝐹 = tpos 𝐺)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1628  tpos ctpos 7516
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1867  ax-4 1882  ax-5 1984  ax-6 2050  ax-7 2086  ax-9 2144  ax-10 2164  ax-11 2179  ax-12 2192  ax-13 2387  ax-ext 2736  ax-sep 4929  ax-nul 4937  ax-pr 5051
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1631  df-ex 1850  df-nf 1855  df-sb 2043  df-clab 2743  df-cleq 2749  df-clel 2752  df-nfc 2887  df-rab 3055  df-v 3338  df-dif 3714  df-un 3716  df-in 3718  df-ss 3725  df-nul 4055  df-if 4227  df-sn 4318  df-pr 4320  df-op 4324  df-br 4801  df-opab 4861  df-mpt 4878  df-xp 5268  df-rel 5269  df-cnv 5270  df-co 5271  df-dm 5272  df-res 5274  df-tpos 7517
This theorem is referenced by:  oppcval  16570  oppchomfval  16571  oppccofval  16573  oppchomfpropd  16583  oppcmon  16595  oppgval  17973  oppgplusfval  17974  oppglsm  18253  opprval  18820  opprmulfval  18821  mattposvs  20459  mattpos1  20460  mamutpos  20462  mattposm  20463  madulid  20649
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