Theorem reldmnmhm 24230

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 24227	. 2 ⊢ NMHom = (𝑠 ∈ NrmMod, 𝑡 ∈ NrmMod ↦ ((𝑠 LMHom 𝑡) ∩ (𝑠 NGHom 𝑡)))
2	1	reldmmpo 7543	1 ⊢ Rel dom NMHom

Syntax hints:   ∩ cin 3948  dom cdm 5677  Rel wrel 5682  (class class class)co 7409   LMHom clmhm 20630  NrmModcnlm 24089   NGHom cnghm 24223   NMHom cnmhm 24224

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704  ax-sep 5300  ax-nul 5307  ax-pr 5428

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-mo 2535  df-eu 2564  df-clab 2711  df-cleq 2725  df-clel 2811  df-nfc 2886  df-rab 3434  df-v 3477  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4324  df-if 4530  df-sn 4630  df-pr 4632  df-op 4636  df-br 5150  df-opab 5212  df-xp 5683  df-rel 5684  df-dm 5687  df-oprab 7413  df-mpo 7414  df-nmhm 24227

This theorem is referenced by: (None)