Theorem biimp3ar 1341

Description: Infer implication from a logical equivalence. Similar to biimpar 295. (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 380	. 2 |- ( ph -> ( ps -> ( th -> ch ) ) )
3	2	3imp 1188	1 |- ( ( ph /\ ps /\ th ) -> ch )

Syntax hints:   -> wi 4   /\ wa 103   <-> wb 104   /\ w3a 973

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 975

This theorem is referenced by:  rmoi  3048  brelrng  4842  ssfzo12  10180  abssubge0  11066  qredeu  12051  basgen2  12875  logbprmirr  13684  lgssq  13735  lgssq2  13736