Theorem stoic1b 1698

Description: Stoic logic Thema 1 (part b). The other part of thema 1 of Stoic logic; see stoic1a 1697. (Contributed by David A. Wheeler, 16-Feb-2019.)

Hypothesis

Ref	Expression
stoic1.1	|- ( ( ph /\ ps ) -> th )

Assertion

Ref	Expression
stoic1b	|- ( ( ps /\ -. th ) -> -. ph )

Proof of Theorem stoic1b

Step	Hyp	Ref	Expression
1		stoic1.1	. . 3 |- ( ( ph /\ ps ) -> th )
2	1	ancoms 469	. 2 |- ( ( ps /\ ph ) -> th )
3	2	stoic1a 1697	1 |- ( ( ps /\ -. th ) -> -. ph )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  hashdomi  13169  hfext  32290