Theorem bisyl8 190

Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise.

Hypotheses

Ref	Expression
bisyl8.1	⊢ (φ → (ψ → (χ → θ)))
bisyl8.2	⊢ (θ ↔ τ)

Assertion

Ref	Expression
bisyl8	⊢ (φ → (ψ → (χ → τ)))

Proof of Theorem bisyl8

Step	Hyp	Ref	Expression
1		bisyl8.1	. 2 ⊢ (φ → (ψ → (χ → θ)))
2		bisyl8.2	. . 3 ⊢ (θ ↔ τ)
3	2	biimp 133	. 2 ⊢ (θ → τ)
4	1, 3	syl8 25	1 ⊢ (φ → (ψ → (χ → τ)))

Syntax hints:   → wi 2   ↔ wb 127

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128

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