Theorem anc2li 552

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 522	1 ⊢ (𝜑 → (𝜓 → (𝜑 ∧ 𝜒)))

Syntax hints:   → wi 4   ∧ wa 385

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 199  df-an 386

This theorem is referenced by:  imdistani  565  pwpw0  4530  sssn  4543  pwsnALT  4619  wfisg  5931  ordtr2  5983  tfis  7286  oeordi  7905  unblem3  8454  trcl  8852  clwlkclwwlkfoOLD  27298  clwlkclwwlkfo  27302  h1datomi  28957  ballotlemfc0  31063  ballotlemfcc  31064  frinsg  32250  dfrdg4  32563  bj-sbsb  33311  clsk1indlem3  39111  sbiota1  39404