Theorem stoic2b 1428

Description: Stoic logic Thema 2 version b. See stoic2a 1427.

Version b is with the phrase "or both". We already have this rule as mpd3an3 1338, so here we prove the equivalence and discourage its use. (New usage is discouraged.) (Contributed by David A. Wheeler, 17-Feb-2019.)

Hypotheses

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

Assertion

Ref	Expression
stoic2b	|- ( ( ph /\ ps ) -> th )

Proof of Theorem stoic2b

Step	Hyp	Ref	Expression
1		stoic2b.1	. 2 |- ( ( ph /\ ps ) -> ch )
2		stoic2b.2	. 2 |- ( ( ph /\ ps /\ ch ) -> th )
3	1, 2	mpd3an3 1338	1 |- ( ( ph /\ ps ) -> th )

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)