Theorem anc2r 249

Description: Conjoin antecedent to right of consequent in nested implication.

Assertion

Ref	Expression
anc2r	⊢ ((φ → (ψ → χ)) → (φ → (ψ → (χ ∧ φ))))

Proof of Theorem anc2r

Step	Hyp	Ref	Expression
1		pm3.21 233	. . 3 ⊢ (φ → (χ → (χ ∧ φ)))
2	1	syl3d 26	. 2 ⊢ (φ → ((ψ → χ) → (ψ → (χ ∧ φ))))
3	2	a2i 8	1 ⊢ ((φ → (ψ → χ)) → (φ → (ψ → (χ ∧ φ))))

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  anc2ri 251  ssorduni 2249

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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