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Theorem funfvdm2f 5181
Description: The value of a function. Version of funfvdm2 5180 using a bound-variable hypotheses instead of distinct variable conditions. (Contributed by Jim Kingdon, 1-Jan-2019.)
Hypotheses
Ref Expression
funfvdm2f.1  F/_
funfvdm2f.2  F/_ F
Assertion
Ref Expression
funfvdm2f  Fun  F  dom  F  F `  U. {  |  F }

Proof of Theorem funfvdm2f
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 funfvdm2 5180 . 2  Fun  F  dom  F  F `  U. {  |  F }
2 funfvdm2f.1 . . . . 5  F/_
3 funfvdm2f.2 . . . . 5  F/_ F
4 nfcv 2175 . . . . 5  F/_
52, 3, 4nfbr 3799 . . . 4  F/  F
6 nfv 1418 . . . 4  F/  F
7 breq2 3759 . . . 4  F  F
85, 6, 7cbvab 2157 . . 3  {  |  F }  {  |  F }
98unieqi 3581 . 2  U. {  |  F }  U. {  |  F }
101, 9syl6eq 2085 1  Fun  F  dom  F  F `  U. {  |  F }
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wceq 1242   wcel 1390   {cab 2023   F/_wnfc 2162   U.cuni 3571   class class class wbr 3755   dom cdm 4288   Fun wfun 4839   ` cfv 4845
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918  ax-pr 3935
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-sbc 2759  df-un 2916  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-opab 3810  df-id 4021  df-xp 4294  df-rel 4295  df-cnv 4296  df-co 4297  df-dm 4298  df-rn 4299  df-res 4300  df-ima 4301  df-iota 4810  df-fun 4847  df-fn 4848  df-fv 4853
This theorem is referenced by: (None)
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