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Theorem thema3 1588
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
thema3.1  |-  ( (
ph  /\  ps )  ->  ch )
thema3.2  |-  ( ( ch  /\  th )  ->  ta )
Assertion
Ref Expression
thema3  |-  ( (
ph  /\  ps  /\  th )  ->  ta )

Proof of Theorem thema3
StepHypRef Expression
1 thema3.1 . . 3  |-  ( (
ph  /\  ps )  ->  ch )
2 thema3.2 . . 3  |-  ( ( ch  /\  th )  ->  ta )
31, 2sylan 471 . 2  |-  ( ( ( ph  /\  ps )  /\  th )  ->  ta )
433impa 1186 1  |-  ( (
ph  /\  ps  /\  th )  ->  ta )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    /\ w3a 968
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 185  df-an 371  df-3an 970
This theorem is referenced by:  ma1repveval  18835  mp2pm2mplem5  19073  cniccibl  21977
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