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Theorem fvmpt3 5500
 Description: Value of a function given in maps-to notation, with a slightly different sethood condition. (Contributed by Stefan O'Rear, 30-Jan-2015.)
Hypotheses
Ref Expression
fvmpt3.a
fvmpt3.b
fvmpt3.c
Assertion
Ref Expression
fvmpt3
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem fvmpt3
StepHypRef Expression
1 fvmpt3.a . . . 4
21eleq1d 2208 . . 3
3 fvmpt3.c . . 3
42, 3vtoclga 2752 . 2
5 fvmpt3.b . . 3
61, 5fvmptg 5497 . 2
74, 6mpdan 417 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1331   wcel 1480   cmpt 3989  cfv 5123 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-pr 4131 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-sbc 2910  df-un 3075  df-in 3077  df-ss 3084  df-pw 3512  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-opab 3990  df-mpt 3991  df-id 4215  df-xp 4545  df-rel 4546  df-cnv 4547  df-co 4548  df-dm 4549  df-iota 5088  df-fun 5125  df-fv 5131 This theorem is referenced by:  fvmpt3i  5501  frec2uzsucd  10174
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