Theorem stoic4b 1409

Description: Stoic logic Thema 4 version b.

This is version b, which is with the phrase "or both". See stoic4a 1408 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 1001	. 2 |- ( ( ph /\ ps /\ th ) -> ch )
3		simp1 981	. 2 |- ( ( ph /\ ps /\ th ) -> ph )
4		simp2 982	. 2 |- ( ( ph /\ ps /\ th ) -> ps )
5		simp3 983	. 2 |- ( ( ph /\ ps /\ th ) -> th )
6		stoic4b.2	. 2 |- ( ( ( ch /\ ph /\ ps ) /\ th ) -> ta )
7	2, 3, 4, 5, 6	syl31anc 1219	1 |- ( ( ph /\ ps /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 962

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 964

This theorem is referenced by: (None)