Theorem impac 304

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 247	. 2 ⊢ (φ → (ψ → (χ ∧ ψ)))
3	2	imp 277	1 ⊢ ((φ ∧ ψ) → (χ ∧ ψ))

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  imdistanri 341  elimant 505  zfrep6 2744  tfrlem5 2953  ac5b 3574  sqr2irr 4782  projlem27 5219

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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