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Theorem stoic4a 1432
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 1433 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 1017 . 2  |-  ( (
ph  /\  ps  /\  th )  ->  ch )
3 simp1 997 . 2  |-  ( (
ph  /\  ps  /\  th )  ->  ph )
4 simp3 999 . 2  |-  ( (
ph  /\  ps  /\  th )  ->  th )
5 stoic4a.2 . 2  |-  ( ( ch  /\  ph  /\  th )  ->  ta )
62, 3, 4, 5syl3anc 1238 1  |-  ( (
ph  /\  ps  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    /\ w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 980
This theorem is referenced by: (None)
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