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  4818  sssn  4831  wfisgOLD  6377  ordtr2  6430  tfis  7876  oeordi  8624  unblem3  9328  trcl  9766  frinsg  9789  clwlkclwwlkfo  30038  h1datomi  31610  ballotlemfc0  34474  ballotlemfcc  34475  pthisspthorcycl  35113  dfrdg4  35933  bj-sbsb  36820  bj-opelidres  37144  clsk1indlem3  44033  sbiota1  44430