Theorem mpid 48

Description: A nested modus ponens deduction.

Hypotheses

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

Assertion

Ref	Expression
mpid	⊢ (φ → (ψ → θ))

Proof of Theorem mpid

Step	Hyp	Ref	Expression
1		mpid.1	. . 3 ⊢ (φ → χ)
2	1	a1d 14	. 2 ⊢ (φ → (ψ → χ))
3		mpid.2	. 2 ⊢ (φ → (ψ → (χ → θ)))
4	2, 3	mpdd 47	1 ⊢ (φ → (ψ → θ))

Syntax hints:   → wi 2

This theorem is referenced by:  mpan2d 525  peano5 2394  sumdmd 5787

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-mp 6

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