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Theorem tposeqd 8159
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 8158 . 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 1541  tpos ctpos 8155
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-12 2171  ax-ext 2707  ax-sep 5256  ax-nul 5263  ax-pr 5384
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-nf 1786  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-rab 3408  df-v 3447  df-dif 3913  df-un 3915  df-in 3917  df-ss 3927  df-nul 4283  df-if 4487  df-sn 4587  df-pr 4589  df-op 4593  df-br 5106  df-opab 5168  df-mpt 5189  df-xp 5639  df-rel 5640  df-cnv 5641  df-co 5642  df-dm 5643  df-res 5645  df-tpos 8156
This theorem is referenced by:  oppcval  17592  oppchomfval  17593  oppchomfvalOLD  17594  oppccofval  17596  oppchomfpropd  17607  oppcmon  17620  oppgval  19123  oppgplusfval  19124  oppglsm  19422  opprval  20048  opprmulfval  20049  mattposvs  21802  mattpos1  21803  mamutpos  21805  mattposm  21806  madulid  21992
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