Description: Deduction adding 7 conjuncts to antecedent. (Contributed by Mario Carneiro, 4-Jan-2017) (Proof shortened by Wolf Lammen, 5-Apr-2022)
Ref | Expression | ||
---|---|---|---|
Hypothesis | ad2ant.1 | |- ( ph -> ps ) |
|
Assertion | ad7antr | |- ( ( ( ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) /\ rh ) -> ps ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad2ant.1 | |- ( ph -> ps ) |
|
2 | 1 | adantr | |- ( ( ph /\ ch ) -> ps ) |
3 | 2 | ad6antr | |- ( ( ( ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) /\ rh ) -> ps ) |