Theorem ancrd 319

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 301	1 ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜓)))

Syntax hints:   → wi 4   ∧ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106

This theorem is referenced by:  impac  373  euan  1997  reupick  3248  prel12  3563  ssrnres  4783  funmo  4937  funssres  4962  dffo4  5336  dffo5  5337  fzospliti  9185  rexuz3  9876  qredeq  10478  prmdvdsfz  10520