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  2125  cgsexg  2795  cgsex2g  2796  cgsex4g  2797  reximdva0m  3462  difsn  3755  preq12b  3796  elres  4978  relssres  4980  fnoprabg  6019  1idprl  7650  1idpru  7651  msqge0  8635  mulge0  8638  fzospliti  10243  algcvga  12189  prmind2  12258  sqrt2irr  12300  grpinveu  13110  metrest  14674  2sqlem10  15212