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Theorem stoic2a 1359
Description: Stoic logic Thema 2 version a.

Statement T2 of [Bobzien] p. 117 shows a reconstructed version of Stoic logic thema 2 as follows: "When from two assertibles a third follows, and from the third and one (or both) of the two another follows, then this other follows from the first two."

Bobzien uses constructs such as  ph, 
ps |-  ch; in Metamath we will represent that construct as  ph 
/\  ps  ->  ch.

This version a is without the phrase "or both"; see stoic2b 1360 for the version with the phrase "or both". We already have this rule as syldan 276, so here we show the equivalence and discourage its use. (New usage is discouraged.) (Contributed by David A. Wheeler, 17-Feb-2019.)

Hypotheses
Ref Expression
stoic2a.1  |-  ( (
ph  /\  ps )  ->  ch )
stoic2a.2  |-  ( (
ph  /\  ch )  ->  th )
Assertion
Ref Expression
stoic2a  |-  ( (
ph  /\  ps )  ->  th )

Proof of Theorem stoic2a
StepHypRef Expression
1 stoic2a.1 . 2  |-  ( (
ph  /\  ps )  ->  ch )
2 stoic2a.2 . 2  |-  ( (
ph  /\  ch )  ->  th )
31, 2syldan 276 1  |-  ( (
ph  /\  ps )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia3 106
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator