**Description:** Equality deduction for operation value. (Contributed by NM, 13-Mar-1995) (Proof shortened by Andrew Salmon, 22-Oct-2011)

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

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

oveq12d.2 | $${\u22a2}{\phi}\to {C}={D}$$ | ||

Assertion | oveq12d | $${\u22a2}{\phi}\to {A}{F}{C}={B}{F}{D}$$ |

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

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

2 | oveq12d.2 | $${\u22a2}{\phi}\to {C}={D}$$ | |

3 | oveq12 | $${\u22a2}\left({A}={B}\wedge {C}={D}\right)\to {A}{F}{C}={B}{F}{D}$$ | |

4 | 1 2 3 | syl2anc | $${\u22a2}{\phi}\to {A}{F}{C}={B}{F}{D}$$ |