Theorem ancrd 537

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 519	1 ⊢ (φ → (ψ → (χ ∧ ψ)))

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:  impac  604  euan  2261  2eu1  2284  reupick  3540  spfininduct  4541  vinf  4556  ssrnres  5060  funssres  5145  dffo4  5424  dffo5  5425