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Theorem tposeqd 6253
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 6252 . 2  |-  ( F  =  G  -> tpos  F  = tpos 
G )
31, 2syl 15 1  |-  ( ph  -> tpos  F  = tpos  G )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1632  tpos ctpos 6249
This theorem is referenced by:  oppchomfpropd  13645
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-opab 4094  df-mpt 4095  df-xp 4711  df-rel 4712  df-cnv 4713  df-co 4714  df-dm 4715  df-res 4717  df-tpos 6250
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