Theorem pm3.35 347

Description: Conjunctive detachment. Theorem *3.35 of [WhiteheadRussell] p. 112. (Contributed by NM, 14-Dec-2002.)

Assertion

Ref	Expression
pm3.35	|- ( ( ph /\ ( ph -> ps ) ) -> ps )

Proof of Theorem pm3.35

Step	Hyp	Ref	Expression
1		pm2.27 40	. 2 |- ( ph -> ( ( ph -> ps ) -> ps ) )
2	1	imp 124	1 |- ( ( ph /\ ( ph -> ps ) ) -> ps )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This theorem is referenced by:  xordc1  1404  19.35-1  1638  ax9o  1712  sbequ8  1861  r19.29af2  2637  r19.29vva  2642  r19.35-1  2647  intab  3903