Theorem stoic4b 1362

Description: Stoic logic Thema 4 version b.

This is version b, which is with the phrase "or both". See stoic4a 1361 for more information. (Contributed by David A. Wheeler, 17-Feb-2019.)

Hypotheses

Ref	Expression
stoic4b.1	|- ( ( ph /\ ps ) -> ch )
stoic4b.2	|- ( ( ( ch /\ ph /\ ps ) /\ th ) -> ta )

Assertion

Ref	Expression
stoic4b	|- ( ( ph /\ ps /\ th ) -> ta )

Proof of Theorem stoic4b

Step	Hyp	Ref	Expression
1		stoic4b.1	. . 3 |- ( ( ph /\ ps ) -> ch )
2	1	3adant3 958	. 2 |- ( ( ph /\ ps /\ th ) -> ch )
3		simp1 938	. 2 |- ( ( ph /\ ps /\ th ) -> ph )
4		simp2 939	. 2 |- ( ( ph /\ ps /\ th ) -> ps )
5		simp3 940	. 2 |- ( ( ph /\ ps /\ th ) -> th )
6		stoic4b.2	. 2 |- ( ( ( ch /\ ph /\ ps ) /\ th ) -> ta )
7	2, 3, 4, 5, 6	syl31anc 1172	1 |- ( ( ph /\ ps /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 102   /\ w3a 919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 921

This theorem is referenced by: (None)