**Description:** A membership and equality inference. (Contributed by NM, 4-Jan-2006)

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

Hypotheses | eqeltrid.1 | $${\u22a2}{A}={B}$$ | |

eqeltrid.2 | $${\u22a2}{\phi}\to {B}\in {C}$$ | ||

Assertion | eqeltrid | $${\u22a2}{\phi}\to {A}\in {C}$$ |

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

1 | eqeltrid.1 | $${\u22a2}{A}={B}$$ | |

2 | eqeltrid.2 | $${\u22a2}{\phi}\to {B}\in {C}$$ | |

3 | 1 | a1i | $${\u22a2}{\phi}\to {A}={B}$$ |

4 | 3 2 | eqeltrd | $${\u22a2}{\phi}\to {A}\in {C}$$ |