Theorem bi2anan9r 844

Description: Deduction joining two equivalences to form equivalence of conjunctions. (Contributed by NM, 19-Feb-1996.)

Hypotheses

Ref	Expression
bi2an9.1	|- (ph -> (ps <-> ch))
bi2an9.2	|- (th -> (ta <-> et))

Assertion

Ref	Expression
bi2anan9r	|- ((th /\ ph) -> ((ps /\ ta) <-> (ch /\ et)))

Proof of Theorem bi2anan9r

Step	Hyp	Ref	Expression
1		bi2an9.1	. . 3 |- (ph -> (ps <-> ch))
2		bi2an9.2	. . 3 |- (th -> (ta <-> et))
3	1, 2	bi2anan9 843	. 2 |- ((ph /\ th) -> ((ps /\ ta) <-> (ch /\ et)))
4	3	ancoms 439	1 |- ((th /\ ph) -> ((ps /\ ta) <-> (ch /\ et)))

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: (None)