Theorem 3syld 11324

Description: Triple syllogism deduction.

Hypotheses

Ref	Expression
3syld.1	⊢ (φ → (ψ → χ))
3syld.2	⊢ (φ → (χ → θ))
3syld.3	⊢ (φ → (θ → τ))

Assertion

Ref	Expression
3syld	⊢ (φ → (ψ → τ))

Proof of Theorem 3syld

Step	Hyp	Ref	Expression
1		3syld.1	. . 3 ⊢ (φ → (ψ → χ))
2		3syld.2	. . 3 ⊢ (φ → (χ → θ))
3	1, 2	syld 27	. 2 ⊢ (φ → (ψ → θ))
4		3syld.3	. 2 ⊢ (φ → (θ → τ))
5	3, 4	syld 27	1 ⊢ (φ → (ψ → τ))

Syntax hints:   → wi 3

This theorem is referenced by:  cnpnei 11472  alexsublem3 11498  comppfsc 11578  cnpfillim 11686

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-mp 7

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