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Theorem ofcfval2 24479
 Description: The function operation expressed as a mapping. (Contributed by Thierry Arnoux, 31-Jan-2017.)
Hypotheses
Ref Expression
ofcfval2.1
ofcfval2.2
ofcfval2.3
ofcfval2.4
Assertion
Ref Expression
ofcfval2 𝑓/𝑐
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem ofcfval2
StepHypRef Expression
1 ofcfval2.3 . . . . 5
21ralrimiva 2781 . . . 4
3 eqid 2435 . . . . 5
43fnmpt 5563 . . . 4
52, 4syl 16 . . 3
6 ofcfval2.4 . . . 4
76fneq1d 5528 . . 3
85, 7mpbird 224 . 2
9 ofcfval2.1 . 2
10 ofcfval2.2 . 2
116, 1fvmpt2d 5806 . 2
128, 9, 10, 11ofcfval 24473 1 𝑓/𝑐
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  wral 2697   cmpt 4258   wfn 5441  (class class class)co 6073  ∘𝑓/𝑐cofc 24470 This theorem is referenced by:  coinflippv  24733 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-rep 4312  ax-sep 4322  ax-nul 4330  ax-pow 4369  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-reu 2704  df-rab 2706  df-v 2950  df-sbc 3154  df-csb 3244  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-iun 4087  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883  df-iota 5410  df-fun 5448  df-fn 5449  df-f 5450  df-f1 5451  df-fo 5452  df-f1o 5453  df-fv 5454  df-ov 6076  df-oprab 6077  df-mpt2 6078  df-ofc 24471
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