Theorem pm3.43i 235

Description: Nested conjunction of antecedents.

Assertion

Ref	Expression
pm3.43i	⊢ ((φ → ψ) → ((φ → χ) → (φ → (ψ ∧ χ))))

Proof of Theorem pm3.43i

Step	Hyp	Ref	Expression
1		pm3.2 232	. . 3 ⊢ (ψ → (χ → (ψ ∧ χ)))
2	1	syl3 18	. 2 ⊢ ((φ → ψ) → (φ → (χ → (ψ ∧ χ))))
3	2	a2d 15	1 ⊢ ((φ → ψ) → ((φ → χ) → (φ → (ψ ∧ χ))))

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  jao 274  ordi 452  ltbtwnpq 3878

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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