Metamath Proof Explorer


Theorem 3imp3i2an

Description: An elimination deduction. (Contributed by Alan Sare, 17-Oct-2017) (Proof shortened by Wolf Lammen, 13-Apr-2022)

Ref Expression
Hypotheses 3imp3i2an.1
|- ( ( ph /\ ps /\ ch ) -> th )
3imp3i2an.2
|- ( ( ph /\ ch ) -> ta )
3imp3i2an.3
|- ( ( th /\ ta ) -> et )
Assertion 3imp3i2an
|- ( ( ph /\ ps /\ ch ) -> et )

Proof

Step Hyp Ref Expression
1 3imp3i2an.1
 |-  ( ( ph /\ ps /\ ch ) -> th )
2 3imp3i2an.2
 |-  ( ( ph /\ ch ) -> ta )
3 3imp3i2an.3
 |-  ( ( th /\ ta ) -> et )
4 2 3adant2
 |-  ( ( ph /\ ps /\ ch ) -> ta )
5 1 4 3 syl2anc
 |-  ( ( ph /\ ps /\ ch ) -> et )