Theorem pm3.1 671

Description: Theorem *3.1 of [WhiteheadRussell] p. 111. The converse holds for decidable propositions, as seen at anordc 863. (Contributed by NM, 3-Jan-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)

Assertion

Ref	Expression
pm3.1	|- ( ( ph /\ ps ) -> -. ( -. ph \/ -. ps ) )

Proof of Theorem pm3.1

Step	Hyp	Ref	Expression
1		pm3.14 670	. 2 |- ( ( -. ph \/ -. ps ) -> -. ( ph /\ ps ) )
2	1	con2i 557	1 |- ( ( ph /\ ps ) -> -. ( -. ph \/ -. ps ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 97   \/ wo 629

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  inssun  3177