Theorem stoic4b 1703

Description: Stoic logic Thema 4 version b. This is version b, which is with the phrase "or both". See stoic4a 1702 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 1081	. 2 |- ( ( ph /\ ps /\ th ) -> ch )
3		simp1 1061	. 2 |- ( ( ph /\ ps /\ th ) -> ph )
4		simp2 1062	. 2 |- ( ( ph /\ ps /\ th ) -> ps )
5		simp3 1063	. 2 |- ( ( ph /\ ps /\ th ) -> th )
6		stoic4b.2	. 2 |- ( ( ( ch /\ ph /\ ps ) /\ th ) -> ta )
7	2, 3, 4, 5, 6	syl31anc 1329	1 |- ( ( ph /\ ps /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 384   /\ w3a 1037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039

This theorem is referenced by: (None)