This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem eelTT1

Description: An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses eelTT1.1 
|- ( T. -> ph )
eelTT1.2 
|- ( T. -> ps )
eelTT1.3 
|- ( ch -> th )
eelTT1.4 
|- ( ( ph /\ ps /\ th ) -> ta )
Assertion eelTT1 
|- ( ch -> ta )

Proof

Step Hyp Ref Expression
1 eelTT1.1 
 |-  ( T. -> ph )
2 eelTT1.2 
 |-  ( T. -> ps )
3 eelTT1.3 
 |-  ( ch -> th )
4 eelTT1.4 
 |-  ( ( ph /\ ps /\ th ) -> ta )
5 3anass 
 |-  ( ( T. /\ T. /\ ch ) <-> ( T. /\ ( T. /\ ch ) ) )
6 anabs5 
 |-  ( ( T. /\ ( T. /\ ch ) ) <-> ( T. /\ ch ) )
7 truan 
 |-  ( ( T. /\ ch ) <-> ch )
8 5 6 7 3bitri 
 |-  ( ( T. /\ T. /\ ch ) <-> ch )
9 1 4 syl3an1 
 |-  ( ( T. /\ ps /\ th ) -> ta )
10 2 9 syl3an2 
 |-  ( ( T. /\ T. /\ th ) -> ta )
11 3 10 syl3an3 
 |-  ( ( T. /\ T. /\ ch ) -> ta )
12 8 11 sylbir 
 |-  ( ch -> ta )