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Theorem tposeqi 7430
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 7399 . 2 (𝐹 = 𝐺 → tpos 𝐹 = tpos 𝐺)
31, 2ax-mp 5 1 tpos 𝐹 = tpos 𝐺
Colors of variables: wff setvar class
Syntax hints:   = wceq 1523  tpos ctpos 7396
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631  ax-sep 4814  ax-nul 4822  ax-pr 4936
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1056  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-rab 2950  df-v 3233  df-dif 3610  df-un 3612  df-in 3614  df-ss 3621  df-nul 3949  df-if 4120  df-sn 4211  df-pr 4213  df-op 4217  df-br 4686  df-opab 4746  df-mpt 4763  df-xp 5149  df-rel 5150  df-cnv 5151  df-co 5152  df-dm 5153  df-res 5155  df-tpos 7397
This theorem is referenced by:  tposoprab  7433  mattpos1  20310
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