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Theorem isoid 6225
 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 5856 . 2
2 fvresi 6097 . . . . 5
3 fvresi 6097 . . . . 5
42, 3breqan12d 4467 . . . 4
54bicomd 201 . . 3
65rgen2a 2884 . 2
7 df-isom 5602 . 2
81, 6, 7mpbir2an 920 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  /\wa 369  e.wcel 1818  A.wral 2807   class class class wbr 4452   cid 4795  |cres 5006  -1-1-onto->wf1o 5592  cfv 5593  Isomwiso 5594 This theorem is referenced by:  ordiso  7962 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017  df-iota 5556  df-fun 5595  df-fn 5596  df-f 5597  df-f1 5598  df-fo 5599  df-f1o 5600  df-fv 5601  df-isom 5602
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