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Theorem tposeqi 7919
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 7888 . 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 1530  tpos ctpos 7885
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2152  ax-12 2167  ax-ext 2796  ax-sep 5199  ax-nul 5206  ax-pr 5325
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-3an 1083  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2803  df-cleq 2817  df-clel 2897  df-nfc 2967  df-rab 3151  df-v 3501  df-dif 3942  df-un 3944  df-in 3946  df-ss 3955  df-nul 4295  df-if 4470  df-sn 4564  df-pr 4566  df-op 4570  df-br 5063  df-opab 5125  df-mpt 5143  df-xp 5559  df-rel 5560  df-cnv 5561  df-co 5562  df-dm 5563  df-res 5565  df-tpos 7886
This theorem is referenced by:  tposoprab  7922  mattpos1  20981
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