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Theorem tposeqi 6104
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 6074 . 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 1299  tpos ctpos 6071
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-14 1460  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082  ax-sep 3986  ax-pow 4038  ax-pr 4069
This theorem depends on definitions:  df-bi 116  df-3an 932  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-ral 2380  df-rex 2381  df-v 2643  df-un 3025  df-in 3027  df-ss 3034  df-pw 3459  df-sn 3480  df-pr 3481  df-op 3483  df-br 3876  df-opab 3930  df-mpt 3931  df-xp 4483  df-rel 4484  df-cnv 4485  df-co 4486  df-dm 4487  df-res 4489  df-tpos 6072
This theorem is referenced by:  tposoprab  6107
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