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))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  spimt  1974  ltfintri  4466  evenoddnnnul  4514  evenodddisj  4516  nnadjoin  4520  sfintfin  4532  tfinnn  4534  nchoicelem17  6305