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Theorem tposeqd 7891
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 7890 . 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 1538  tpos ctpos 7887
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-sep 5189  ax-nul 5196  ax-pr 5317
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-rab 3142  df-v 3482  df-dif 3922  df-un 3924  df-in 3926  df-ss 3936  df-nul 4277  df-if 4451  df-sn 4551  df-pr 4553  df-op 4557  df-br 5053  df-opab 5115  df-mpt 5133  df-xp 5548  df-rel 5549  df-cnv 5550  df-co 5551  df-dm 5552  df-res 5554  df-tpos 7888
This theorem is referenced by:  oppcval  16983  oppchomfval  16984  oppccofval  16986  oppchomfpropd  16996  oppcmon  17008  oppgval  18475  oppgplusfval  18476  oppglsm  18767  opprval  19377  opprmulfval  19378  mattposvs  21067  mattpos1  21068  mamutpos  21070  mattposm  21071  madulid  21257
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