Metamath Proof Explorer


Theorem stoic2b

Description: Stoic logic Thema 2 version b. See stoic2a . Version b is with the phrase "or both". We already have this rule as mpd3an3 , so here we prove the equivalence and discourage its use. (New usage is discouraged.) (Contributed by David A. Wheeler, 17-Feb-2019)

Ref Expression
Hypotheses stoic2b.1
|- ( ( ph /\ ps ) -> ch )
stoic2b.2
|- ( ( ph /\ ps /\ ch ) -> th )
Assertion stoic2b
|- ( ( ph /\ ps ) -> th )

Proof

Step Hyp Ref Expression
1 stoic2b.1
 |-  ( ( ph /\ ps ) -> ch )
2 stoic2b.2
 |-  ( ( ph /\ ps /\ ch ) -> th )
3 1 2 mpd3an3
 |-  ( ( ph /\ ps ) -> th )