Theorem exbiri 605

Description: Inference form of exbir 1365. This proof is exbiriVD in set.mm automatically translated and minimized. (Contributed by Alan Sare, 31-Dec-2011.) (Proof shortened by Wolf Lammen, 27-Jan-2013.)

Hypothesis

Ref	Expression
exbiri.1	⊢ ((φ ∧ ψ) → (χ ↔ θ))

Assertion

Ref	Expression
exbiri	⊢ (φ → (ψ → (θ → χ)))

Proof of Theorem exbiri

Step	Hyp	Ref	Expression
1		exbiri.1	. . 3 ⊢ ((φ ∧ ψ) → (χ ↔ θ))
2	1	biimpar 471	. 2 ⊢ (((φ ∧ ψ) ∧ θ) → χ)
3	2	exp31 587	1 ⊢ (φ → (ψ → (θ → 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:  biimp3ar  1282  eqrdav  2352  ncfin  6248