Theorem biadan2 623

Description: Add a conjunction to an equivalence. (Contributed by Jeff Madsen, 20-Jun-2011.)

Hypotheses

Ref	Expression
biadan2.1	|- (ph -> ps)
biadan2.2	|- (ps -> (ph <-> ch))

Assertion

Ref	Expression
biadan2	|- (ph <-> (ps /\ ch))

Proof of Theorem biadan2

Step	Hyp	Ref	Expression
1		biadan2.1	. . 3 |- (ph -> ps)
2	1	pm4.71ri 614	. 2 |- (ph <-> (ps /\ ph))
3		biadan2.2	. . 3 |- (ps -> (ph <-> ch))
4	3	pm5.32i 618	. 2 |- ((ps /\ ph) <-> (ps /\ ch))
5	2, 4	bitri 240	1 |- (ph <-> (ps /\ ch))

Syntax hints:   -> wi 4   <-> wb 176   /\ wa 358

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 177  df-an 360

This theorem is referenced by:  elab4g  2990  eqpw1  4163  eqnc2  6130