Description: Introduce a left anti-conjunct to both sides of a logical equivalence. (Contributed by Anthony Hart, 1-Sep-2011) (Proof shortened by SF, 2-Jan-2018)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | nanbi2 | |- ( ( ph <-> ps ) -> ( ( ch -/\ ph ) <-> ( ch -/\ ps ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nanbi1 | |- ( ( ph <-> ps ) -> ( ( ph -/\ ch ) <-> ( ps -/\ ch ) ) ) |
|
| 2 | nancom | |- ( ( ch -/\ ph ) <-> ( ph -/\ ch ) ) |
|
| 3 | nancom | |- ( ( ch -/\ ps ) <-> ( ps -/\ ch ) ) |
|
| 4 | 1 2 3 | 3bitr4g | |- ( ( ph <-> ps ) -> ( ( ch -/\ ph ) <-> ( ch -/\ ps ) ) ) |