Theorem mp3an2ani 1380

Description: An elimination deduction. (Contributed by Alan Sare, 17-Oct-2017.)

Hypotheses

Ref	Expression
mp3an2ani.1	|- ph
mp3an2ani.2	|- ( ps -> ch )
mp3an2ani.3	|- ( ( ps /\ th ) -> ta )
mp3an2ani.4	|- ( ( ph /\ ch /\ ta ) -> et )

Assertion

Ref	Expression
mp3an2ani	|- ( ( ps /\ th ) -> et )

Proof of Theorem mp3an2ani

Step	Hyp	Ref	Expression
1		mp3an2ani.1	. . 3 |- ph
2		mp3an2ani.2	. . 3 |- ( ps -> ch )
3		mp3an2ani.3	. . 3 |- ( ( ps /\ th ) -> ta )
4		mp3an2ani.4	. . 3 |- ( ( ph /\ ch /\ ta ) -> et )
5	1, 2, 3, 4	mp3an3an 1379	. 2 |- ( ( ps /\ ( ps /\ th ) ) -> et )
6	5	anabss5 580	1 |- ( ( ps /\ th ) -> et )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1004

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 1006

This theorem is referenced by:  tfr1onlemubacc  6512  tfrcllemubacc  6525  mappsrprg  8024  seqclg  10735  seqfeq4g  10794  wrdexg  11128  plusffng  13466  mulgnngsum  13732  ellspsn  14450  metrest  15249  2lgsoddprmlem2  15854