Theorem embantd 50

Description: Deduction embedding an antecedent. (Contributed by Wolf Lammen, 4-Oct-2013.)

Hypotheses

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

Assertion

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

Proof of Theorem embantd

Step	Hyp	Ref	Expression
1		embantd.1	. 2 ⊢ (φ → ψ)
2		embantd.2	. . 3 ⊢ (φ → (χ → θ))
3	2	imim2d 48	. 2 ⊢ (φ → ((ψ → χ) → (ψ → θ)))
4	1, 3	mpid 37	1 ⊢ (φ → ((ψ → χ) → θ))

This proof depends on syntax axioms:   → wi 4

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

This theorem is used by:  spimt  1974  ltfintri  4467  evenoddnnnul  4515  evenodddisj  4517  nnadjoin  4521  sfintfin  4533  tfinnn  4535  nchoicelem17  6306