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Theorem fvmpt2i 5803
 Description: Value of a function given by the "maps to" notation. (Contributed by Mario Carneiro, 23-Apr-2014.)
Hypothesis
Ref Expression
fvmpt2.1
Assertion
Ref Expression
fvmpt2i
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem fvmpt2i
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbeq1 3246 . . 3
2 csbid 3250 . . 3
31, 2syl6eq 2483 . 2
4 fvmpt2.1 . . 3
5 nfcv 2571 . . . 4
6 nfcsb1v 3275 . . . 4
7 csbeq1a 3251 . . . 4
85, 6, 7cbvmpt 4291 . . 3
94, 8eqtri 2455 . 2
103, 9fvmpti 5797 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  csb 3243   cmpt 4258   cid 4485  cfv 5446 This theorem is referenced by:  fvmpt2  5804  sumfc  12495  fsumf1o  12509  sumss  12510  isumshft  12611  mbfsup  19548  itg2splitlem  19632  dgrle  20154  prodfc  25263  fprodf1o  25264 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-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-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-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-fv 5454
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