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Theorem tposeqd 6411
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 6410 . 2  |-  ( F  =  G  -> tpos  F  = tpos 
G )
31, 2syl 16 1  |-  ( ph  -> tpos  F  = tpos  G )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649  tpos ctpos 6407
This theorem is referenced by:  oppcval  13859  oppchomfval  13860  oppccofval  13862  oppchomfpropd  13872  oppcmon  13884  oppgval  15063  oppgplusfval  15064  oppglsm  15196  opprval  15649  opprmulfval  15650
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361  ax-sep 4264  ax-nul 4272  ax-pr 4337
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-ne 2545  df-ral 2647  df-rex 2648  df-rab 2651  df-v 2894  df-dif 3259  df-un 3261  df-in 3263  df-ss 3270  df-nul 3565  df-if 3676  df-sn 3756  df-pr 3757  df-op 3759  df-br 4147  df-opab 4201  df-mpt 4202  df-xp 4817  df-rel 4818  df-cnv 4819  df-co 4820  df-dm 4821  df-res 4823  df-tpos 6408
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