Theorem anc2li 557

Description: Deduction conjoining antecedent to left of consequent in nested implication. (Contributed by NM, 10-Aug-1994.) (Proof shortened by Wolf Lammen, 7-Dec-2012.)

Hypothesis

Ref	Expression
anc2li.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
anc2li	|- ( ph -> ( ps -> ( ph /\ ch ) ) )

Proof of Theorem anc2li

Step	Hyp	Ref	Expression
1		anc2li.1	. 2 |- ( ph -> ( ps -> ch ) )
2		id 22	. 2 |- ( ph -> ph )
3	1, 2	jctild 543	1 |- ( ph -> ( ps -> ( ph /\ ch ) ) )

Syntax hints:   -> wi 4   /\ wa 369

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 185  df-an 371

This theorem is referenced by:  imdistani  690  pwpw0  4116  sssn  4126  pwsnALT  4181  ordtr2  4858  tfis  6562  oeordi  7123  unblem3  7664  trcl  8046  h1datomi  25116  ballotlemfc0  27006  ballotlemfcc  27007  wfisg  27801  frinsg  27837  dfrdg4  28112  sbiota1  29823