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Theorem stoic4a 1337
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  th to represent the "external" assertibles. This is version a, which is without the phrase "or both"; see stoic4b 1338 for the version with the phrase "or both". (Contributed by David A. Wheeler, 17-Feb-2019.)

Hypotheses
Ref Expression
stoic4a.1  |-  ( (
ph  /\  ps )  ->  ch )
stoic4a.2  |-  ( ( ch  /\  ph  /\  th )  ->  ta )
Assertion
Ref Expression
stoic4a  |-  ( (
ph  /\  ps  /\  th )  ->  ta )

Proof of Theorem stoic4a
StepHypRef Expression
1 stoic4a.1 . . 3  |-  ( (
ph  /\  ps )  ->  ch )
213adant3 935 . 2  |-  ( (
ph  /\  ps  /\  th )  ->  ch )
3 simp1 915 . 2  |-  ( (
ph  /\  ps  /\  th )  ->  ph )
4 simp3 917 . 2  |-  ( (
ph  /\  ps  /\  th )  ->  th )
5 stoic4a.2 . 2  |-  ( ( ch  /\  ph  /\  th )  ->  ta )
62, 3, 4, 5syl3anc 1146 1  |-  ( (
ph  /\  ps  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101    /\ w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by: (None)
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