Theorem biimp3ar 1282

Description: Infer implication from a logical equivalence. Similar to biimpar 471. (Contributed by NM, 2-Jan-2009.)

Hypothesis

Ref	Expression
biimp3a.1	|- ((ph /\ ps) -> (ch <-> th))

Assertion

Ref	Expression
biimp3ar	|- ((ph /\ ps /\ th) -> ch)

Proof of Theorem biimp3ar

Step	Hyp	Ref	Expression
1		biimp3a.1	. . 3 |- ((ph /\ ps) -> (ch <-> th))
2	1	exbiri 605	. 2 |- (ph -> (ps -> (th -> ch)))
3	2	3imp 1145	1 |- ((ph /\ ps /\ th) -> ch)

Syntax hints:   -> wi 4   <-> wb 176   /\ wa 358   /\ w3a 934

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  df-3an 936

This theorem is referenced by:  rmoi  3136  ovmpt2x  5713  ceclr  6188