Theorem reldmnmhm 24674

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

Assertion

Ref	Expression
reldmnmhm	⊢ Rel dom NMHom

Proof of Theorem reldmnmhm

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

Step	Hyp	Ref	Expression
1		df-nmhm 24671	. 2 ⊢ NMHom = (𝑠 ∈ NrmMod, 𝑡 ∈ NrmMod ↦ ((𝑠 LMHom 𝑡) ∩ (𝑠 NGHom 𝑡)))
2	1	reldmmpo 7555	1 ⊢ Rel dom NMHom

Syntax hints:   ∩ cin 3943  dom cdm 5678  Rel wrel 5683  (class class class)co 7419   LMHom clmhm 20916  NrmModcnlm 24533   NGHom cnghm 24667   NMHom cnmhm 24668

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 2166  ax-ext 2696  ax-sep 5300  ax-nul 5307  ax-pr 5429

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  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 2703  df-cleq 2717  df-clel 2802  df-nfc 2877  df-rab 3419  df-v 3463  df-dif 3947  df-un 3949  df-ss 3961  df-nul 4323  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-br 5150  df-opab 5212  df-xp 5684  df-rel 5685  df-dm 5688  df-oprab 7423  df-mpo 7424  df-nmhm 24671

This theorem is referenced by: (None)