Theorem ancrd 326

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 307	1 ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜓)))

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:  impac  381  euan  2101  reupick  3447  prel12  3801  ssrnres  5112  funmo  5273  funssres  5300  dffo4  5710  dffo5  5711  fzospliti  10252  rexuz3  11155  qredeq  12264  prmdvdsfz  12307