**Description:** Equality deduction for operation value. (Contributed by NM, 10-Aug-1995)

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

Hypotheses | oveq1d.1 | $${\u22a2}{\phi}\to {A}={B}$$ | |

opreqan12i.2 | $${\u22a2}{\psi}\to {C}={D}$$ | ||

Assertion | oveqan12rd | $${\u22a2}\left({\psi}\wedge {\phi}\right)\to {A}{F}{C}={B}{F}{D}$$ |

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

1 | oveq1d.1 | $${\u22a2}{\phi}\to {A}={B}$$ | |

2 | opreqan12i.2 | $${\u22a2}{\psi}\to {C}={D}$$ | |

3 | 1 2 | oveqan12d | $${\u22a2}\left({\phi}\wedge {\psi}\right)\to {A}{F}{C}={B}{F}{D}$$ |

4 | 3 | ancoms | $${\u22a2}\left({\psi}\wedge {\phi}\right)\to {A}{F}{C}={B}{F}{D}$$ |