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Theorem tposeqi 6479
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 6448 . 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 1649  tpos ctpos 6445
This theorem is referenced by:  tposoprab  6482
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 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393  ax-sep 4298  ax-nul 4306  ax-pr 4371
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 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-ne 2577  df-ral 2679  df-rex 2680  df-rab 2683  df-v 2926  df-dif 3291  df-un 3293  df-in 3295  df-ss 3302  df-nul 3597  df-if 3708  df-sn 3788  df-pr 3789  df-op 3791  df-br 4181  df-opab 4235  df-mpt 4236  df-xp 4851  df-rel 4852  df-cnv 4853  df-co 4854  df-dm 4855  df-res 4857  df-tpos 6446
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