Theorem reldmnghm 24584

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 24581	. 2 ⊢ NGHom = (𝑠 ∈ NrmGrp, 𝑡 ∈ NrmGrp ↦ (◡(𝑠 normOp 𝑡) “ ℝ))
2	1	reldmmpo 7539	1 ⊢ Rel dom NGHom

Syntax hints:  ^◡ccnv 5668  dom cdm 5669   “ cima 5672  Rel wrel 5674  (class class class)co 7405  ℝcr 11111  NrmGrpcngp 24441   normOp cnmo 24577   NGHom cnghm 24578

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2163  ax-ext 2697  ax-sep 5292  ax-nul 5299  ax-pr 5420

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2528  df-eu 2557  df-clab 2704  df-cleq 2718  df-clel 2804  df-nfc 2879  df-rab 3427  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-br 5142  df-opab 5204  df-xp 5675  df-rel 5676  df-dm 5679  df-oprab 7409  df-mpo 7410  df-nghm 24581

This theorem is referenced by: (None)