Theorem biimpac 472

Description: Inference from a logical equivalence. (Contributed by NM, 3-May-1994.)

Hypothesis

Ref	Expression
biimpa.1	⊢ (φ → (ψ ↔ χ))

Assertion

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

Proof of Theorem biimpac

Step	Hyp	Ref	Expression
1		biimpa.1	. . 3 ⊢ (φ → (ψ ↔ χ))
2	1	biimpcd 215	. 2 ⊢ (ψ → (φ → χ))
3	2	imp 418	1 ⊢ ((ψ ∧ φ) → χ)

Syntax hints:   → wi 4   ↔ wb 176   ∧ 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:  gencbvex2  2903  2reu5  3045  vfinspsslem1  4551  phi11lem1  4596  0cnelphi  4598  ideqg2  4870  nfunsn  5354  leltctr  6213  tlecg  6231  nchoicelem3  6292