MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  tposeqi Structured version   Unicode version

Theorem tposeqi 6541
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 6510 . 2  |-  ( F  =  G  -> tpos  F  = tpos 
G )
31, 2ax-mp 5 1  |- tpos  F  = tpos 
G
Colors of variables: wff set class
Syntax hints:    = wceq 1653  tpos ctpos 6507
This theorem is referenced by:  tposoprab  6544
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-14 1731  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-sep 4355  ax-nul 4363  ax-pr 4432
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-ral 2716  df-rex 2717  df-rab 2720  df-v 2964  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-op 3847  df-br 4238  df-opab 4292  df-mpt 4293  df-xp 4913  df-rel 4914  df-cnv 4915  df-co 4916  df-dm 4917  df-res 4919  df-tpos 6508
  Copyright terms: Public domain W3C validator