Theorem biimp3a 1281

Description: Infer implication from a logical equivalence. Similar to biimpa 470. (Contributed by NM, 4-Sep-2005.)

Hypothesis

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

Assertion

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

Proof of Theorem biimp3a

Step	Hyp	Ref	Expression
1		biimp3a.1	. . 3 |- ((ph /\ ps) -> (ch <-> th))
2	1	biimpa 470	. 2 |- (((ph /\ ps) /\ ch) -> th)
3	2	3impa 1146	1 |- ((ph /\ ps /\ ch) -> th)

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: (None)