ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  stoic3 Unicode version

Theorem stoic3 1361
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
StepHypRef Expression
1 stoic3.1 . . 3  |-  ( (
ph  /\  ps )  ->  ch )
2 stoic3.2 . . 3  |-  ( ( ch  /\  th )  ->  ta )
31, 2sylan 277 . 2  |-  ( ( ( ph  /\  ps )  /\  th )  ->  ta )
433impa 1134 1  |-  ( (
ph  /\  ps  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    /\ w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by:  f1imaeng  6360  absdiflt  10179  absdifle  10180
  Copyright terms: Public domain W3C validator