Theorem mpii 45

Description: A doubly nested modus ponens inference.

Hypotheses

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

Assertion

Ref	Expression
mpii	⊢ (φ → (ψ → θ))

Proof of Theorem mpii

Step	Hyp	Ref	Expression
1		mpii.1	. 2 ⊢ χ
2		mpii.2	. . 3 ⊢ (φ → (ψ → (χ → θ)))
3	2	com23 32	. 2 ⊢ (φ → (χ → (ψ → θ)))
4	1, 3	mpi 44	1 ⊢ (φ → (ψ → θ))

Syntax hints:   → wi 2

This theorem is referenced by:  mpan2i 522  intmin 1982  frirr 2176  ssorduni 2249  suceloni 2314  tfrlem1 2949  rankr1lem 3517  rankval3 3525  bndrank 3526

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

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