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)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108

This theorem is used by:  impac  381  euan  2143  reupick  3517  prel12  3896  ssrelrn  4972  ssrnres  5230  funmo  5392  funssres  5420  dffo4  5856  dffo5  5857  en2prde  7539  fzospliti  10585  rexuz3  11756  qredeq  12874  prmdvdsfz  12917