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Theorem tposeqd 7507
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 7506 . 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 1631  tpos ctpos 7503
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751  ax-sep 4915  ax-nul 4923  ax-pr 5034
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-3an 1073  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-rab 3070  df-v 3353  df-dif 3726  df-un 3728  df-in 3730  df-ss 3737  df-nul 4064  df-if 4226  df-sn 4317  df-pr 4319  df-op 4323  df-br 4787  df-opab 4847  df-mpt 4864  df-xp 5255  df-rel 5256  df-cnv 5257  df-co 5258  df-dm 5259  df-res 5261  df-tpos 7504
This theorem is referenced by:  oppcval  16580  oppchomfval  16581  oppccofval  16583  oppchomfpropd  16593  oppcmon  16605  oppgval  17984  oppgplusfval  17985  oppglsm  18264  opprval  18832  opprmulfval  18833  mattposvs  20479  mattpos1  20480  mamutpos  20482  mattposm  20483  madulid  20669
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