Theorem tposeqi 8189

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

Step	Hyp	Ref	Expression
1		tposeqi.1	. 2 ⊢ 𝐹 = 𝐺
2		tposeq 8158	. 2 ⊢ (𝐹 = 𝐺 → tpos 𝐹 = tpos 𝐺)
3	1, 2	ax-mp 5	1 ⊢ tpos 𝐹 = tpos 𝐺

Syntax hints:   = wceq 1541  tpos ctpos 8155

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-10 2144  ax-12 2180  ax-ext 2703  ax-sep 5234  ax-nul 5244  ax-pr 5370

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-nf 1785  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-rab 3396  df-v 3438  df-dif 3905  df-un 3907  df-in 3909  df-ss 3919  df-nul 4284  df-if 4476  df-sn 4577  df-pr 4579  df-op 4583  df-br 5092  df-opab 5154  df-mpt 5173  df-xp 5622  df-rel 5623  df-cnv 5624  df-co 5625  df-dm 5626  df-res 5628  df-tpos 8156

This theorem is referenced by:  tposoprab  8192  mattpos1  22372  opprabs  33445  tposresxp  48920