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Theorem stoic4a 1408
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 1409 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 1001 . 2  |-  ( (
ph  /\  ps  /\  th )  ->  ch )
3 simp1 981 . 2  |-  ( (
ph  /\  ps  /\  th )  ->  ph )
4 simp3 983 . 2  |-  ( (
ph  /\  ps  /\  th )  ->  th )
5 stoic4a.2 . 2  |-  ( ( ch  /\  ph  /\  th )  ->  ta )
62, 3, 4, 5syl3anc 1216 1  |-  ( (
ph  /\  ps  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 962
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 964
This theorem is referenced by: (None)
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