**Description:** Add right intersection to subclass relation. (Contributed by Glauco
Siliprandi, 2-Jan-2022)

Ref | Expression | ||
---|---|---|---|

Hypothesis | ssrind.1 | $${\u22a2}{\phi}\to {A}\subseteq {B}$$ | |

Assertion | ssrind | $${\u22a2}{\phi}\to {A}\cap {C}\subseteq {B}\cap {C}$$ |

Step | Hyp | Ref | Expression |
---|---|---|---|

1 | ssrind.1 | $${\u22a2}{\phi}\to {A}\subseteq {B}$$ | |

2 | ssrin | $${\u22a2}{A}\subseteq {B}\to {A}\cap {C}\subseteq {B}\cap {C}$$ | |

3 | 1 2 | syl | $${\u22a2}{\phi}\to {A}\cap {C}\subseteq {B}\cap {C}$$ |