Theorem stoic3 1431

Description: Stoic logic Thema 3.

Statement T3 of [Bobzien] p. 116-117 discusses Stoic logic thema 3.

"When from two (assemblies) a third follows, and from the one that follows (i.e., the third) together with another, external external assumption, another follows, then other follows from the first two and the externally co-assumed one. (Simp. Cael. 237.2-4)" (Contributed by David A. Wheeler, 17-Feb-2019.)

Hypotheses

Ref	Expression
stoic3.1	|- ( ( ph /\ ps ) -> ch )
stoic3.2	|- ( ( ch /\ th ) -> ta )

Assertion

Ref	Expression
stoic3	|- ( ( ph /\ ps /\ th ) -> ta )

Proof of Theorem stoic3

Step	Hyp	Ref	Expression
1		stoic3.1	. . 3 |- ( ( ph /\ ps ) -> ch )
2		stoic3.2	. . 3 |- ( ( ch /\ th ) -> ta )
3	1, 2	sylan 283	. 2 |- ( ( ( ph /\ ps ) /\ th ) -> ta )
4	3	3impa 1194	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:  f1imaeng  6789  absdiflt  11094  absdifle  11095  xrmaxlesup  11260  fsumdifsnconst  11456  cos01gt0  11763  opnneiss  13529  cxpmul  14204