**Description:** Multiplication by 0. Theorem I.6 of Apostol p. 18. (Contributed by Mario Carneiro, 27-May-2016)

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

Hypothesis | muld.1 | $${\u22a2}{\phi}\to {A}\in \u2102$$ | |

Assertion | mul02d | $${\u22a2}{\phi}\to 0\cdot {A}=0$$ |

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

1 | muld.1 | $${\u22a2}{\phi}\to {A}\in \u2102$$ | |

2 | mul02 | $${\u22a2}{A}\in \u2102\to 0\cdot {A}=0$$ | |

3 | 1 2 | syl | $${\u22a2}{\phi}\to 0\cdot {A}=0$$ |