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Theorem rnghmresel 39308
 Description: An element of the non-unital ring homomorphisms restricted to a subset of non-unital rings is a non-unital ring homomorphisms. (Contributed by AV, 9-Mar-2020.)
Hypothesis
Ref Expression
rnghmresel.h RngHomo
Assertion
Ref Expression
rnghmresel RngHomo

Proof of Theorem rnghmresel
StepHypRef Expression
1 rnghmresel.h . . . . . 6 RngHomo
21adantr 467 . . . . 5 RngHomo
32oveqd 6320 . . . 4 RngHomo
4 ovres 6448 . . . . 5 RngHomo RngHomo
54adantl 468 . . . 4 RngHomo RngHomo
63, 5eqtrd 2464 . . 3 RngHomo
76eleq2d 2493 . 2 RngHomo
87biimp3a 1365 1 RngHomo
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 371   w3a 983   wceq 1438   wcel 1869   cxp 4849   cres 4853  (class class class)co 6303   RngHomo crngh 39227 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-9 1873  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054  ax-ext 2401  ax-sep 4544  ax-nul 4553  ax-pr 4658 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 985  df-tru 1441  df-ex 1661  df-nf 1665  df-sb 1788  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2573  df-ne 2621  df-ral 2781  df-rex 2782  df-rab 2785  df-v 3084  df-dif 3440  df-un 3442  df-in 3444  df-ss 3451  df-nul 3763  df-if 3911  df-sn 3998  df-pr 4000  df-op 4004  df-uni 4218  df-br 4422  df-opab 4481  df-xp 4857  df-res 4863  df-iota 5563  df-fv 5607  df-ov 6306 This theorem is referenced by:  rnghmsubcsetclem2  39320
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