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Theorem fvmptf 5479
 Description: Value of a function given by an ordered-pair class abstraction. This version of fvmptg 5463 uses bound-variable hypotheses instead of distinct variable conditions. (Contributed by NM, 8-Nov-2005.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
fvmptf.1
fvmptf.2
fvmptf.3
fvmptf.4
Assertion
Ref Expression
fvmptf
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()   ()   ()

Proof of Theorem fvmptf
StepHypRef Expression
1 elex 2669 . . 3
2 fvmptf.1 . . . 4
3 fvmptf.2 . . . . . 6
43nfel1 2267 . . . . 5
5 fvmptf.4 . . . . . . . 8
6 nfmpt1 3989 . . . . . . . 8
75, 6nfcxfr 2253 . . . . . . 7
87, 2nffv 5397 . . . . . 6
98, 3nfeq 2264 . . . . 5
104, 9nfim 1534 . . . 4
11 fvmptf.3 . . . . . 6
1211eleq1d 2184 . . . . 5
13 fveq2 5387 . . . . . 6
1413, 11eqeq12d 2130 . . . . 5
1512, 14imbi12d 233 . . . 4
165fvmpt2 5470 . . . . 5
1716ex 114 . . . 4
182, 10, 15, 17vtoclgaf 2723 . . 3
191, 18syl5 32 . 2
2019imp 123 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1314   wcel 1463  wnfc 2243  cvv 2658   cmpt 3957  cfv 5091 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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-14 1475  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-sep 4014  ax-pow 4066  ax-pr 4099 This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-eu 1978  df-mo 1979  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-ral 2396  df-rex 2397  df-v 2660  df-sbc 2881  df-csb 2974  df-un 3043  df-in 3045  df-ss 3052  df-pw 3480  df-sn 3501  df-pr 3502  df-op 3504  df-uni 3705  df-br 3898  df-opab 3958  df-mpt 3959  df-id 4183  df-xp 4513  df-rel 4514  df-cnv 4515  df-co 4516  df-dm 4517  df-iota 5056  df-fun 5093  df-fv 5099 This theorem is referenced by:  fvmptd3  5480  elfvmptrab1  5481  sumrbdclem  11096  fsum3  11107  isumss  11111
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