Description: Expanded definition of parallel product. (Contributed by Scott Fenton, 3-May-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | dfpprod2 | |- pprod ( A , B ) = ( ( `' ( 1st |` ( _V X. _V ) ) o. ( A o. ( 1st |` ( _V X. _V ) ) ) ) i^i ( `' ( 2nd |` ( _V X. _V ) ) o. ( B o. ( 2nd |` ( _V X. _V ) ) ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-pprod | |- pprod ( A , B ) = ( ( A o. ( 1st |` ( _V X. _V ) ) ) (x) ( B o. ( 2nd |` ( _V X. _V ) ) ) ) |
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2 | df-txp | |- ( ( A o. ( 1st |` ( _V X. _V ) ) ) (x) ( B o. ( 2nd |` ( _V X. _V ) ) ) ) = ( ( `' ( 1st |` ( _V X. _V ) ) o. ( A o. ( 1st |` ( _V X. _V ) ) ) ) i^i ( `' ( 2nd |` ( _V X. _V ) ) o. ( B o. ( 2nd |` ( _V X. _V ) ) ) ) ) |
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3 | 1 2 | eqtri | |- pprod ( A , B ) = ( ( `' ( 1st |` ( _V X. _V ) ) o. ( A o. ( 1st |` ( _V X. _V ) ) ) ) i^i ( `' ( 2nd |` ( _V X. _V ) ) o. ( B o. ( 2nd |` ( _V X. _V ) ) ) ) ) |