Theorem ancld 325

Description: Deduction conjoining antecedent to left of consequent in nested implication. (Contributed by NM, 15-Aug-1994.) (Proof shortened by Wolf Lammen, 1-Nov-2012.)

Hypothesis

Ref	Expression
ancld.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

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

Proof of Theorem ancld

Step	Hyp	Ref	Expression
1		idd 21	. 2 ⊢ (𝜑 → (𝜓 → 𝜓))
2		ancld.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
3	1, 2	jcad 307	1 ⊢ (𝜑 → (𝜓 → (𝜓 ∧ 𝜒)))

Syntax hints:   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108

This theorem is referenced by:  mopick2  2136  cgsexg  2806  cgsex2g  2807  cgsex4g  2808  reximdva0m  3475  difsn  3769  preq12b  3810  elres  4992  relssres  4994  fnoprabg  6036  1idprl  7685  1idpru  7686  msqge0  8671  mulge0  8674  fzospliti  10281  algcvga  12292  prmind2  12361  sqrt2irr  12403  grpinveu  13288  metrest  14896  2sqlem10  15520