Description: Deduction adding a conjunct to antecedent. (Contributed by Glauco Siliprandi, 11-Dec-2019)
Ref | Expression | ||
---|---|---|---|
Hypothesis | 3adantlr3.1 | |- ( ( ( ph /\ ( ps /\ ch ) ) /\ th ) -> ta ) |
|
Assertion | 3adantlr3 | |- ( ( ( ph /\ ( ps /\ ch /\ et ) ) /\ th ) -> ta ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3adantlr3.1 | |- ( ( ( ph /\ ( ps /\ ch ) ) /\ th ) -> ta ) |
|
2 | simpll | |- ( ( ( ph /\ ( ps /\ ch /\ et ) ) /\ th ) -> ph ) |
|
3 | simplr1 | |- ( ( ( ph /\ ( ps /\ ch /\ et ) ) /\ th ) -> ps ) |
|
4 | simplr2 | |- ( ( ( ph /\ ( ps /\ ch /\ et ) ) /\ th ) -> ch ) |
|
5 | 3 4 | jca | |- ( ( ( ph /\ ( ps /\ ch /\ et ) ) /\ th ) -> ( ps /\ ch ) ) |
6 | simpr | |- ( ( ( ph /\ ( ps /\ ch /\ et ) ) /\ th ) -> th ) |
|
7 | 2 5 6 1 | syl21anc | |- ( ( ( ph /\ ( ps /\ ch /\ et ) ) /\ th ) -> ta ) |