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Theorem tposeqi 6351
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 6320 . 2  |-  ( F  =  G  -> tpos  F  = tpos 
G )
31, 2ax-mp 8 1  |- tpos  F  = tpos 
G
Colors of variables: wff set class
Syntax hints:    = wceq 1642  tpos ctpos 6317
This theorem is referenced by:  tposoprab  6354
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-14 1714  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339  ax-sep 4220  ax-nul 4228  ax-pr 4293
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ne 2523  df-ral 2624  df-rex 2625  df-rab 2628  df-v 2866  df-dif 3231  df-un 3233  df-in 3235  df-ss 3242  df-nul 3532  df-if 3642  df-sn 3722  df-pr 3723  df-op 3725  df-br 4103  df-opab 4157  df-mpt 4158  df-xp 4774  df-rel 4775  df-cnv 4776  df-co 4777  df-dm 4778  df-res 4780  df-tpos 6318
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