Theorem tposeqd 8248

Description: Equality theorem for transposition. (Contributed by Mario Carneiro, 7-Jan-2017.)

Hypothesis

Ref	Expression
tposeqd.1	⊢ (𝜑 → 𝐹 = 𝐺)

Assertion

Ref	Expression
tposeqd	⊢ (𝜑 → tpos 𝐹 = tpos 𝐺)

Proof of Theorem tposeqd

Step	Hyp	Ref	Expression
1		tposeqd.1	. 2 ⊢ (𝜑 → 𝐹 = 𝐺)
2		tposeq 8247	. 2 ⊢ (𝐹 = 𝐺 → tpos 𝐹 = tpos 𝐺)
3	1, 2	syl 17	1 ⊢ (𝜑 → tpos 𝐹 = tpos 𝐺)

Syntax hints:   → wi 4   = wceq 1534  tpos ctpos 8244

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2102  ax-9 2110  ax-10 2133  ax-12 2170  ax-ext 2700  ax-sep 5305  ax-nul 5312  ax-pr 5435

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1537  df-fal 1547  df-ex 1775  df-nf 1779  df-sb 2062  df-clab 2707  df-cleq 2721  df-clel 2806  df-rab 3429  df-v 3474  df-dif 3961  df-un 3963  df-in 3965  df-ss 3975  df-nul 4334  df-if 4535  df-sn 4635  df-pr 4637  df-op 4641  df-br 5155  df-opab 5217  df-mpt 5238  df-xp 5690  df-rel 5691  df-cnv 5692  df-co 5693  df-dm 5694  df-res 5696  df-tpos 8245

This theorem is referenced by:  oppcval  17739  oppchomfval  17740  oppchomfvalOLD  17741  oppccofval  17743  oppchomfpropd  17754  oppcmon  17767  oppgval  19355  oppgplusfval  19356  oppglsm  19652  opprval  20329  opprmulfval  20330  mattposvs  22448  mattpos1  22449  mamutpos  22451  mattposm  22452  madulid  22638