Theorem reldmnghm 24772

Description: Lemma for normed group homomorphisms. (Contributed by Mario Carneiro, 18-Oct-2015.)

Assertion

Ref	Expression
reldmnghm	⊢ Rel dom NGHom

Proof of Theorem reldmnghm

Dummy variables 𝑠 𝑡 are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-nghm 24769	. 2 ⊢ NGHom = (𝑠 ∈ NrmGrp, 𝑡 ∈ NrmGrp ↦ (◡(𝑠 normOp 𝑡) “ ℝ))
2	1	reldmmpo 7530	1 ⊢ Rel dom NGHom

Syntax hints:  ^◡ccnv 5646  dom cdm 5647   “ cima 5650  Rel wrel 5652  (class class class)co 7396  ℝcr 11072  NrmGrpcngp 24637   normOp cnmo 24765   NGHom cnghm 24766

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815  ax-4 1829  ax-5 1930  ax-6 1987  ax-7 2028  ax-8 2144  ax-9 2152  ax-10 2175  ax-11 2191  ax-12 2212  ax-ext 2734  ax-sep 5246  ax-pr 5390

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-3an 1100  df-tru 1563  df-fal 1573  df-ex 1800  df-nf 1804  df-sb 2091  df-mo 2566  df-eu 2596  df-clab 2741  df-cleq 2754  df-clel 2837  df-nfc 2911  df-rab 3415  df-v 3456  df-dif 3907  df-un 3909  df-in 3911  df-ss 3921  df-nul 4286  df-if 4481  df-sn 4583  df-pr 4585  df-op 4589  df-br 5101  df-opab 5163  df-xp 5653  df-rel 5654  df-dm 5657  df-oprab 7400  df-mpo 7401  df-nghm 24769

This theorem is referenced by: (None)