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Theorem offveq 6327
 Description: Convert an identity of the operation to the analogous identity on the function operation. (Contributed by Mario Carneiro, 24-Jul-2014.)
Hypotheses
Ref Expression
offveq.1
offveq.2
offveq.3
offveq.4
offveq.5
offveq.6
offveq.7
Assertion
Ref Expression
offveq
Distinct variable groups:   ,   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem offveq
StepHypRef Expression
1 offveq.2 . . 3
2 offveq.3 . . 3
3 offveq.1 . . 3
4 inidm 3552 . . 3
51, 2, 3, 3, 4offn 6318 . 2
6 offveq.4 . 2
7 offveq.5 . . . 4
8 offveq.6 . . . 4
91, 2, 3, 3, 4, 7, 8ofval 6316 . . 3
10 offveq.7 . . 3
119, 10eqtrd 2470 . 2
125, 6, 11eqfnfvd 5832 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726   wfn 5451  cfv 5456  (class class class)co 6083   cof 6305 This theorem is referenced by:  caofid0l  6334  caofid0r  6335  caofid1  6336  caofid2  6337  ofnegsub  10000  bddibl  19733  dvaddf  19830  plydivlem3  20214  ofsubid  27520  ofmul12  27521  ofdivrec  27522  ofdivcan4  27523  ofdivdiv2  27524 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-rep 4322  ax-sep 4332  ax-nul 4340  ax-pow 4379  ax-pr 4405 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-reu 2714  df-rab 2716  df-v 2960  df-sbc 3164  df-csb 3254  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-iun 4097  df-br 4215  df-opab 4269  df-mpt 4270  df-id 4500  df-xp 4886  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-rn 4891  df-res 4892  df-ima 4893  df-iota 5420  df-fun 5458  df-fn 5459  df-f 5460  df-f1 5461  df-fo 5462  df-f1o 5463  df-fv 5464  df-ov 6086  df-oprab 6087  df-mpt2 6088  df-of 6307
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