Description: Join two logical equivalences with anti-conjunction. (Contributed by Scott Fenton, 2-Jan-2018)
Ref | Expression | ||
---|---|---|---|
Hypotheses | nanbid.1 | |- ( ph -> ( ps <-> ch ) ) |
|
nanbi12d.2 | |- ( ph -> ( th <-> ta ) ) |
||
Assertion | nanbi12d | |- ( ph -> ( ( ps -/\ th ) <-> ( ch -/\ ta ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nanbid.1 | |- ( ph -> ( ps <-> ch ) ) |
|
2 | nanbi12d.2 | |- ( ph -> ( th <-> ta ) ) |
|
3 | nanbi12 | |- ( ( ( ps <-> ch ) /\ ( th <-> ta ) ) -> ( ( ps -/\ th ) <-> ( ch -/\ ta ) ) ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> ( ( ps -/\ th ) <-> ( ch -/\ ta ) ) ) |