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Theorem rngohomf 26596
 Description: A ring homomorphism is a function. (Contributed by Jeff Madsen, 19-Jun-2010.)
Hypotheses
Ref Expression
rnghomf.1
rnghomf.2
rnghomf.3
rnghomf.4
Assertion
Ref Expression
rngohomf

Proof of Theorem rngohomf
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 rnghomf.1 . . . . 5
2 eqid 2438 . . . . 5
3 rnghomf.2 . . . . 5
4 eqid 2438 . . . . 5 GId GId
5 rnghomf.3 . . . . 5
6 eqid 2438 . . . . 5
7 rnghomf.4 . . . . 5
8 eqid 2438 . . . . 5 GId GId
91, 2, 3, 4, 5, 6, 7, 8isrngohom 26595 . . . 4 GId GId
109biimpa 472 . . 3 GId GId
1110simp1d 970 . 2
12113impa 1149 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   w3a 937   wceq 1653   wcel 1726  wral 2707   crn 4882  wf 5453  cfv 5457  (class class class)co 6084  c1st 6350  c2nd 6351  GIdcgi 21780  crngo 21968   crnghom 26590 This theorem is referenced by:  rngohomcl  26597  rngogrphom  26601  rngohomco  26604  keridl  26656 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pow 4380  ax-pr 4406  ax-un 4704 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-opab 4270  df-id 4501  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-rn 4892  df-iota 5421  df-fun 5459  df-fn 5460  df-f 5461  df-fv 5465  df-ov 6087  df-oprab 6088  df-mpt2 6089  df-map 7023  df-rngohom 26593
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