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Theorem stoic4a 1610
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 to represent the "external" assertibles. This is version a, which is without the phrase "or both"; see stoic4b 1611 for the version with the phrase "or both". (Contributed by David A. Wheeler, 17-Feb-2019.)

Hypotheses
Ref Expression
stoic4a.1
stoic4a.2
Assertion
Ref Expression
stoic4a

Proof of Theorem stoic4a
StepHypRef Expression
1 stoic4a.1 . . 3
213adant3 1016 . 2
3 simp1 996 . 2
4 simp3 998 . 2
5 stoic4a.2 . 2
62, 3, 4, 5syl3anc 1228 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  /\w3a 973
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 975
  Copyright terms: Public domain W3C validator