Theorem stoic4a 1321

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 1322 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 924	. 2 |- ( ( ph /\ ps /\ th ) -> ch )
3		simp1 904	. 2 |- ( ( ph /\ ps /\ th ) -> ph )
4		simp3 906	. 2 |- ( ( ph /\ ps /\ th ) -> th )
5		stoic4a.2	. 2 |- ( ( ch /\ ph /\ th ) -> ta )
6	2, 3, 4, 5	syl3anc 1135	1 |- ( ( ph /\ ps /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 97   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by: (None)