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Theorem tposeqi 5926
Description: Equality theorem for transposition. (Contributed by Mario Carneiro, 10-Sep-2015.)
Hypothesis
Ref Expression
tposeqi.1  |-  F  =  G
Assertion
Ref Expression
tposeqi  |- tpos  F  = tpos 
G

Proof of Theorem tposeqi
StepHypRef Expression
1 tposeqi.1 . 2  |-  F  =  G
2 tposeq 5896 . 2  |-  ( F  =  G  -> tpos  F  = tpos 
G )
31, 2ax-mp 7 1  |- tpos  F  = tpos 
G
Colors of variables: wff set class
Syntax hints:    = wceq 1285  tpos ctpos 5893
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956  ax-pr 3972
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794  df-opab 3848  df-mpt 3849  df-xp 4377  df-rel 4378  df-cnv 4379  df-co 4380  df-dm 4381  df-res 4383  df-tpos 5894
This theorem is referenced by:  tposoprab  5929
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