Theorem reldmnmhm 24691

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 24688	. 2 ⊢ NMHom = (𝑠 ∈ NrmMod, 𝑡 ∈ NrmMod ↦ ((𝑠 LMHom 𝑡) ∩ (𝑠 NGHom 𝑡)))
2	1	reldmmpo 7495	1 ⊢ Rel dom NMHom

Syntax hints:   ∩ cin 3889  dom cdm 5625  Rel wrel 5630  (class class class)co 7361   LMHom clmhm 21009  NrmModcnlm 24558   NGHom cnghm 24684   NMHom cnmhm 24685

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-10 2147  ax-11 2163  ax-12 2185  ax-ext 2709  ax-sep 5232  ax-pr 5371

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-nf 1786  df-sb 2069  df-mo 2540  df-eu 2570  df-clab 2716  df-cleq 2729  df-clel 2812  df-nfc 2886  df-rab 3391  df-v 3432  df-dif 3893  df-un 3895  df-in 3897  df-ss 3907  df-nul 4275  df-if 4468  df-sn 4569  df-pr 4571  df-op 4575  df-br 5087  df-opab 5149  df-xp 5631  df-rel 5632  df-dm 5635  df-oprab 7365  df-mpo 7366  df-nmhm 24688

This theorem is referenced by: (None)