Theorem ancld 536

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 519	1 ⊢ (φ → (ψ → (ψ ∧ χ)))

Syntax hints:   → wi 4   ∧ wa 358

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 177  df-an 360

This theorem is referenced by:  mopick2  2271  cgsexg  2891  cgsex2g  2892  cgsex4g  2893  reximdva0  3562  difsn  3846  preq12b  4128  nnpw1ex  4485  tfin11  4494  vinf  4556  dmcosseq  4974  ssreseq  4998  fnoprabg  5586  dmfrec  6317