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Theorem isoid 6012
 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 5676 . 2
2 fvresi 5887 . . . . 5
3 fvresi 5887 . . . . 5
42, 3breqan12d 4191 . . . 4
54bicomd 193 . . 3
65rgen2a 2736 . 2
7 df-isom 5426 . 2
81, 6, 7mpbir2an 887 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wcel 1721  wral 2670   class class class wbr 4176   cid 4457   cres 4843  wf1o 5416  cfv 5417   wiso 5418 This theorem is referenced by:  ordiso  7445 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389  ax-sep 4294  ax-nul 4302  ax-pr 4367 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2262  df-mo 2263  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-ne 2573  df-ral 2675  df-rex 2676  df-rab 2679  df-v 2922  df-sbc 3126  df-dif 3287  df-un 3289  df-in 3291  df-ss 3298  df-nul 3593  df-if 3704  df-sn 3784  df-pr 3785  df-op 3787  df-uni 3980  df-br 4177  df-opab 4231  df-id 4462  df-xp 4847  df-rel 4848  df-cnv 4849  df-co 4850  df-dm 4851  df-rn 4852  df-res 4853  df-ima 4854  df-iota 5381  df-fun 5419  df-fn 5420  df-f 5421  df-f1 5422  df-fo 5423  df-f1o 5424  df-fv 5425  df-isom 5426
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