Theorem impac 387

Description: Importation with conjunction in consequent.

Hypothesis

Ref	Expression
impac.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
impac	⊢ ((φ ⋀ ψ) → (χ ⋀ ψ))

Proof of Theorem impac

Step	Hyp	Ref	Expression
1		impac.1	. . 3 ⊢ (φ → (ψ → χ))
2	1	ancrd 299	. 2 ⊢ (φ → (ψ → (χ ⋀ ψ)))
3	2	imp 350	1 ⊢ ((φ ⋀ ψ) → (χ ⋀ ψ))

Syntax hints:   → wi 3   ⋀ wa 223

This theorem is referenced by:  imdistanri 444  zfrep6 3600  tfrlem5 3900  ac5b 4725  sqr2irr 6659  fsumsplit 6958  projlem27 9128

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

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