Theorem biimp3ar 1357

Description: Infer implication from a logical equivalence. Similar to biimpar 297. (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 382	. 2 |- ( ph -> ( ps -> ( th -> ch ) ) )
3	2	3imp 1195	1 |- ( ( ph /\ ps /\ th ) -> ch )

Syntax hints:   -> wi 4   /\ wa 104   <-> wb 105   /\ w3a 980

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 982

This theorem is referenced by:  rmoi  3083  brelrng  4897  ssfzo12  10300  abssubge0  11267  qredeu  12265  basgen2  14317  logbprmirr  15208  lgssq  15281  lgssq2  15282