Description: Dominance law for Cartesian product. Theorem 6L(c) of Enderton p. 149. (Contributed by NM, 28-Sep-2004) (Revised by NM, 29-Mar-2006) (Revised by Mario Carneiro, 7-May-2015)
Ref | Expression | ||
---|---|---|---|
Hypothesis | xpdom1.2 | |- C e. _V |
|
Assertion | xpdom1 | |- ( A ~<_ B -> ( A X. C ) ~<_ ( B X. C ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpdom1.2 | |- C e. _V |
|
2 | xpdom1g | |- ( ( C e. _V /\ A ~<_ B ) -> ( A X. C ) ~<_ ( B X. C ) ) |
|
3 | 1 2 | mpan | |- ( A ~<_ B -> ( A X. C ) ~<_ ( B X. C ) ) |