Theorem anc2li 555

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	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
anc2li	⊢ (𝜑 → (𝜓 → (𝜑 ∧ 𝜒)))

Proof of Theorem anc2li

Step	Hyp	Ref	Expression
1		anc2li.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		id 22	. 2 ⊢ (𝜑 → 𝜑)
3	1, 2	jctild 525	1 ⊢ (𝜑 → (𝜓 → (𝜑 ∧ 𝜒)))

Syntax hints:   → wi 4   ∧ wa 395

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 207  df-an 396

This theorem is referenced by:  imdistani  568  pwpw0  4780  sssn  4793  ordtr2  6380  tfis  7834  oeordi  8554  unblem3  9248  trcl  9688  frinsg  9711  pthisspthorcycl  29739  clwlkclwwlkfo  29945  h1datomi  31517  ballotlemfc0  34491  ballotlemfcc  34492  dfrdg4  35946  bj-sbsb  36832  bj-opelidres  37156  clsk1indlem3  44039  sbiota1  44430