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Theorem isoid 6238
 Description: Identity law for isomorphism. Proposition 6.30(1) of [TakeutiZaring] p. 33. (Contributed by NM, 27-Apr-2004.)
Assertion
Ref Expression
isoid

Proof of Theorem isoid
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 f1oi 5864 . 2
2 fvresi 6106 . . . . 5
3 fvresi 6106 . . . . 5
42, 3breqan12d 4411 . . . 4
54bicomd 206 . . 3
65rgen2a 2820 . 2
7 df-isom 5598 . 2
81, 6, 7mpbir2an 934 1
 Colors of variables: wff setvar class Syntax hints:   wb 189   wa 376   wcel 1904  wral 2756   class class class wbr 4395   cid 4749   cres 4841  wf1o 5588  cfv 5589   wiso 5590 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-sbc 3256  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-uni 4191  df-br 4396  df-opab 4455  df-id 4754  df-xp 4845  df-rel 4846  df-cnv 4847  df-co 4848  df-dm 4849  df-rn 4850  df-res 4851  df-ima 4852  df-iota 5553  df-fun 5591  df-fn 5592  df-f 5593  df-f1 5594  df-fo 5595  df-f1o 5596  df-fv 5597  df-isom 5598 This theorem is referenced by:  ordiso  8049
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