Description: The "proves" relation on a set. A wff encoded as U is true in a model M iff for every valuation s e. ( M ^m _om ) , the interpretation of the wff using the membership relation on M is true. (Contributed by AV, 5-Nov-2023)
Ref | Expression | ||
---|---|---|---|
Assertion | prv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq12 | ||
2 | simpl | ||
3 | 2 | oveq1d | |
4 | 1 3 | eqeq12d | |
5 | df-prv | ||
6 | 4 5 | brabga |