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Theorem tposeqi 7954
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 7923 . 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 1542  tpos ctpos 7920
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-8 2116  ax-9 2124  ax-10 2145  ax-12 2179  ax-ext 2710  ax-sep 5167  ax-nul 5174  ax-pr 5296
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1787  df-nf 1791  df-sb 2075  df-clab 2717  df-cleq 2730  df-clel 2811  df-rab 3062  df-v 3400  df-dif 3846  df-un 3848  df-in 3850  df-ss 3860  df-nul 4212  df-if 4415  df-sn 4517  df-pr 4519  df-op 4523  df-br 5031  df-opab 5093  df-mpt 5111  df-xp 5531  df-rel 5532  df-cnv 5533  df-co 5534  df-dm 5535  df-res 5537  df-tpos 7921
This theorem is referenced by:  tposoprab  7957  mattpos1  21207
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