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Theorem stoic3 1407
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 281 . 2  |-  ( ( ( ph  /\  ps )  /\  th )  ->  ta )
433impa 1176 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:  f1imaeng  6686  absdiflt  10876  absdifle  10877  xrmaxlesup  11040  fsumdifsnconst  11236  cos01gt0  11480  opnneiss  12341  cxpmul  13012
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