Theorem ancrd 309

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

Hypothesis

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

Assertion

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

Proof of Theorem ancrd

Step	Hyp	Ref	Expression
1		ancrd.1	. 2 ⊢ (φ → (ψ → χ))
2		idd 21	. 2 ⊢ (φ → (ψ → ψ))
3	1, 2	jcad 291	1 ⊢ (φ → (ψ → (χ ∧ ψ)))

Syntax hints:   → wi 4   ∧ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101

This theorem is referenced by:  impac  363  euan  1953  reupick  3215  prel12  3533  ssrnres  4706  funmo  4860  funssres  4885  dffo4  5258  dffo5  5259  fzospliti  8802