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Theorem fveleq 26203
Description: Please add description here. (Contributed by Jeff Hoffman, 12-Feb-2008.)
Assertion
Ref Expression
fveleq  |-  ( A  =  B  ->  (
( ph  ->  ( F `
 A )  e.  P )  <->  ( ph  ->  ( F `  B
)  e.  P ) ) )

Proof of Theorem fveleq
StepHypRef Expression
1 fveq2 5730 . . 3  |-  ( A  =  B  ->  ( F `  A )  =  ( F `  B ) )
21eleq1d 2504 . 2  |-  ( A  =  B  ->  (
( F `  A
)  e.  P  <->  ( F `  B )  e.  P
) )
32imbi2d 309 1  |-  ( A  =  B  ->  (
( ph  ->  ( F `
 A )  e.  P )  <->  ( ph  ->  ( F `  B
)  e.  P ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178    = wceq 1653    e. wcel 1726   ` cfv 5456
This theorem is referenced by:  findfvcl  26204
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-iota 5420  df-fv 5464
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