**Description:** Identity law for multiplication. (Contributed by Mario Carneiro, 27-May-2016)

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

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

Assertion | mulid2d | $${\u22a2}{\phi}\to 1{A}={A}$$ |

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

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

2 | mulid2 | $${\u22a2}{A}\in \u2102\to 1{A}={A}$$ | |

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