Theorem simplbi2 608

Description: Deduction eliminating a conjunct. Automatically derived from simplbi2VD in set.mm. (Contributed by Alan Sare, 31-Dec-2011.)

Hypothesis

Ref	Expression
pm3.26bi2.1	⊢ (φ ↔ (ψ ∧ χ))

Assertion

Ref	Expression
simplbi2	⊢ (ψ → (χ → φ))

Proof of Theorem simplbi2

Step	Hyp	Ref	Expression
1		pm3.26bi2.1	. . 3 ⊢ (φ ↔ (ψ ∧ χ))
2	1	biimpri 197	. 2 ⊢ ((ψ ∧ χ) → φ)
3	2	ex 423	1 ⊢ (ψ → (χ → φ))

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:  simplbi2com  1374  sspss  3369  neldif  3392  reuss2  3536  pssdifn0  3612  sfinltfin  4536