Theorem stoic4a 1702

Description: Stoic logic Thema 4 version a. Statement T4 of [Bobzien] p. 117 shows a reconstructed version of Stoic logic Thema 4: "When from two assertibles a third follows, and from the third and one (or both) of the two and one (or more) external assertible(s) another follows, then this other follows from the first two and the external(s)."

We use th to represent the "external" assertibles. This is version a, which is without the phrase "or both"; see stoic4b 1703 for the version with the phrase "or both". (Contributed by David A. Wheeler, 17-Feb-2019.)

Hypotheses

Ref	Expression
stoic4a.1	|- ( ( ph /\ ps ) -> ch )
stoic4a.2	|- ( ( ch /\ ph /\ th ) -> ta )

Assertion

Ref	Expression
stoic4a	|- ( ( ph /\ ps /\ th ) -> ta )

Proof of Theorem stoic4a

Step	Hyp	Ref	Expression
1		stoic4a.1	. . 3 |- ( ( ph /\ ps ) -> ch )
2	1	3adant3 1081	. 2 |- ( ( ph /\ ps /\ th ) -> ch )
3		simp1 1061	. 2 |- ( ( ph /\ ps /\ th ) -> ph )
4		simp3 1063	. 2 |- ( ( ph /\ ps /\ th ) -> th )
5		stoic4a.2	. 2 |- ( ( ch /\ ph /\ th ) -> ta )
6	2, 3, 4, 5	syl3anc 1326	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)