Theorem mpdd 47

Description: A nested modus ponens deduction.

Hypotheses

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

Assertion

Ref	Expression
mpdd	⊢ (φ → (ψ → θ))

Proof of Theorem mpdd

Step	Hyp	Ref	Expression
1		mpdd.1	. 2 ⊢ (φ → (ψ → χ))
2		mpdd.2	. . 3 ⊢ (φ → (ψ → (χ → θ)))
3	2	a2d 15	. 2 ⊢ (φ → ((ψ → χ) → (ψ → θ)))
4	1, 3	mpd 46	1 ⊢ (φ → (ψ → θ))

Syntax hints:   → wi 2

This theorem is referenced by:  mpid 48  syldd 50  oaordex 3160  oaass 3163  omordi 3164  nnmord 3189  brecop 3242  sumdmdlem 5786

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

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