Theorem syland 352

Description: A syllogism deduction.

Hypotheses

Ref	Expression
syland.1	⊢ (φ → ((ψ ∧ χ) → θ))
syland.2	⊢ (φ → (τ → ψ))

Assertion

Ref	Expression
syland	⊢ (φ → ((τ ∧ χ) → θ))

Proof of Theorem syland

Step	Hyp	Ref	Expression
1		syland.2	. . 3 ⊢ (φ → (τ → ψ))
2		syland.1	. . . 4 ⊢ (φ → ((ψ ∧ χ) → θ))
3	2	exp3a 292	. . 3 ⊢ (φ → (ψ → (χ → θ)))
4	1, 3	syld 27	. 2 ⊢ (φ → (τ → (χ → θ)))
5	4	imp3a 279	1 ⊢ (φ → ((τ ∧ χ) → θ))

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  sylan2d 353  syl2and 354  sylani 356

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  df-an 198

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