Theorem biimparc 473

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

Hypothesis

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

Assertion

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

Proof of Theorem biimparc

Step	Hyp	Ref	Expression
1		biimpa.1	. . 3 ⊢ (φ → (ψ ↔ χ))
2	1	biimprcd 216	. 2 ⊢ (χ → (φ → ψ))
3	2	imp 418	1 ⊢ ((χ ∧ φ) → ψ)

This proof depends on syntax axioms:   → wi 4   ↔ wb 176   ∧ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by:  biantr  897  difprsnss  3847  fun11iun  5306  eqfnfv2  5394  fmpt  5693