Theorem anclb 530

Description: Conjoin antecedent to left of consequent. Theorem *4.7 of [WhiteheadRussell] p. 120. (Contributed by NM, 25-Jul-1999.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)

Assertion

Ref	Expression
anclb	|- ((ph -> ps) <-> (ph -> (ph /\ ps)))

Proof of Theorem anclb

Step	Hyp	Ref	Expression
1		ibar 490	. 2 |- (ph -> (ps <-> (ph /\ ps)))
2	1	pm5.74i 236	1 |- ((ph -> ps) <-> (ph -> (ph /\ ps)))

This proof depends on syntax axioms:   -> wi 4   <-> wb 176   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by:  pm4.71  611  difin  3493