Theorem im2anan9r 881

Description: Deduction joining nested implications to form implication of conjunctions. (Contributed by NM, 29-Feb-1996.)

Hypotheses

Ref	Expression
im2an9.1	|- ( ph -> ( ps -> ch ) )
im2an9.2	|- ( th -> ( ta -> et ) )

Assertion

Ref	Expression
im2anan9r	|- ( ( th /\ ph ) -> ( ( ps /\ ta ) -> ( ch /\ et ) ) )

Proof of Theorem im2anan9r

Step	Hyp	Ref	Expression
1		im2an9.1	. . 3 |- ( ph -> ( ps -> ch ) )
2		im2an9.2	. . 3 |- ( th -> ( ta -> et ) )
3	1, 2	im2anan9 880	. 2 |- ( ( ph /\ th ) -> ( ( ps /\ ta ) -> ( ch /\ et ) ) )
4	3	ancoms 469	1 |- ( ( th /\ ph ) -> ( ( ps /\ ta ) -> ( ch /\ et ) ) )

Syntax hints:   -> wi 4   /\ wa 384

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 197  df-an 386

This theorem is referenced by:  pssnn  8178  lbreu  10973  catideu  16336  exidu1  33655  rngoideu  33702