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Mirrors > Home > NFE Home > Th. List > df-pprod | GIF version |
Description: Define the parallel product operation. (Contributed by SF, 9-Feb-2015.) |
Ref | Expression |
---|---|
df-pprod | ⊢ PProd (A, B) = ((A ∘ 1^{st} ) ⊗ (B ∘ 2^{nd} )) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class A | |
2 | cB | . . 3 class B | |
3 | 1, 2 | cpprod 5737 | . 2 class PProd (A, B) |
4 | c1st 4717 | . . . 4 class 1^{st} | |
5 | 1, 4 | ccom 4721 | . . 3 class (A ∘ 1^{st} ) |
6 | c2nd 4783 | . . . 4 class 2^{nd} | |
7 | 2, 6 | ccom 4721 | . . 3 class (B ∘ 2^{nd} ) |
8 | 5, 7 | ctxp 5735 | . 2 class ((A ∘ 1^{st} ) ⊗ (B ∘ 2^{nd} )) |
9 | 3, 8 | wceq 1642 | 1 wff PProd (A, B) = ((A ∘ 1^{st} ) ⊗ (B ∘ 2^{nd} )) |
Colors of variables: wff setvar class |
This definition is referenced by: pprodeq1 5834 pprodeq2 5835 qrpprod 5836 pprodexg 5837 brpprod 5839 cnvpprod 5841 |
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