Description: Lemma for fin1a2 . (Contributed by Stefan O'Rear, 7-Nov-2014)
Ref | Expression | ||
---|---|---|---|
Hypothesis | fin1a2lem.b | |- E = ( x e. _om |-> ( 2o .o x ) ) |
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Assertion | fin1a2lem3 | |- ( A e. _om -> ( E ` A ) = ( 2o .o A ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fin1a2lem.b | |- E = ( x e. _om |-> ( 2o .o x ) ) |
|
2 | oveq2 | |- ( a = A -> ( 2o .o a ) = ( 2o .o A ) ) |
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3 | oveq2 | |- ( x = a -> ( 2o .o x ) = ( 2o .o a ) ) |
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4 | 3 | cbvmptv | |- ( x e. _om |-> ( 2o .o x ) ) = ( a e. _om |-> ( 2o .o a ) ) |
5 | 1 4 | eqtri | |- E = ( a e. _om |-> ( 2o .o a ) ) |
6 | ovex | |- ( 2o .o A ) e. _V |
|
7 | 2 5 6 | fvmpt | |- ( A e. _om -> ( E ` A ) = ( 2o .o A ) ) |