Theorem stoic4b 1433

Description: Stoic logic Thema 4 version b.

This is version b, which is with the phrase "or both". See stoic4a 1432 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 1017	. 2 |- ( ( ph /\ ps /\ th ) -> ch )
3		simp1 997	. 2 |- ( ( ph /\ ps /\ th ) -> ph )
4		simp2 998	. 2 |- ( ( ph /\ ps /\ th ) -> ps )
5		simp3 999	. 2 |- ( ( ph /\ ps /\ th ) -> th )
6		stoic4b.2	. 2 |- ( ( ( ch /\ ph /\ ps ) /\ th ) -> ta )
7	2, 3, 4, 5, 6	syl31anc 1241	1 |- ( ( ph /\ ps /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 978

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 980

This theorem is referenced by: (None)