Theorem stoic3 1419

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 281	. 2 |- ( ( ( ph /\ ps ) /\ th ) -> ta )
4	3	3impa 1184	1 |- ( ( ph /\ ps /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 968

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 970

This theorem is referenced by:  f1imaeng  6758  absdiflt  11034  absdifle  11035  xrmaxlesup  11200  fsumdifsnconst  11396  cos01gt0  11703  opnneiss  12798  cxpmul  13473