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Theorem fveq1 5120
Description: Equality theorem for function value. (Contributed by NM, 29-Dec-1996.)
Assertion
Ref Expression
fveq1  F  G  F `  G `

Proof of Theorem fveq1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 breq 3757 . . 3  F  G  F  G
21iotabidv 4831 . 2  F  G  iota F  iota G
3 df-fv 4853 . 2  F `
 iota F
4 df-fv 4853 . 2  G `
 iota G
52, 3, 43eqtr4g 2094 1  F  G  F `  G `
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242   class class class wbr 3755   iotacio 4808   ` 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-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853
This theorem is referenced by:  fveq1i  5122  fveq1d  5123  fvmptdf  5201  fvmptdv2  5203  isoeq1  5384  oveq  5461  offval  5661  ofrfval  5662  offval3  5703  smoeq  5846  recseq  5862  tfr0  5878  tfrlemiex  5886  rdgeq1  5898  rdgivallem  5908  rdg0  5914  frec0g  5922  frecsuclem3  5929  frecsuc  5930  1fv  8726  iseqeq3  8856
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