Theorem jad 154

Description: Deduction form of ja 153. (Contributed by Scott Fenton, 13-Dec-2010.) (Proof shortened by Andrew Salmon, 17-Sep-2011.)

Hypotheses

Ref	Expression
jad.1	⊢ (φ → (¬ ψ → θ))
jad.2	⊢ (φ → (χ → θ))

Assertion

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

Proof of Theorem jad

Step	Hyp	Ref	Expression
1		jad.1	. . . 4 ⊢ (φ → (¬ ψ → θ))
2	1	com12 27	. . 3 ⊢ (¬ ψ → (φ → θ))
3		jad.2	. . . 4 ⊢ (φ → (χ → θ))
4	3	com12 27	. . 3 ⊢ (χ → (φ → θ))
5	2, 4	ja 153	. 2 ⊢ ((ψ → χ) → (φ → θ))
6	5	com12 27	1 ⊢ (φ → ((ψ → χ) → θ))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

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

This theorem is used by:  pm2.6  162  pm2.65  164  merco2  1501  nfimdOLD  1809  hbimdOLD  1816  ax11indi  2196