Theorem tposeqi 8046

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 8015	. 2 ⊢ (𝐹 = 𝐺 → tpos 𝐹 = tpos 𝐺)
3	1, 2	ax-mp 5	1 ⊢ tpos 𝐹 = tpos 𝐺

Syntax hints:   = wceq 1539  tpos ctpos 8012

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-10 2139  ax-12 2173  ax-ext 2709  ax-sep 5218  ax-nul 5225  ax-pr 5347

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-3an 1087  df-tru 1542  df-fal 1552  df-ex 1784  df-nf 1788  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-rab 3072  df-v 3424  df-dif 3886  df-un 3888  df-in 3890  df-ss 3900  df-nul 4254  df-if 4457  df-sn 4559  df-pr 4561  df-op 4565  df-br 5071  df-opab 5133  df-mpt 5154  df-xp 5586  df-rel 5587  df-cnv 5588  df-co 5589  df-dm 5590  df-res 5592  df-tpos 8013

This theorem is referenced by:  tposoprab  8049  mattpos1  21513