Theorem imdistanri 341

Description: Distribution of implication with conjunction.

Hypothesis

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

Assertion

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

Proof of Theorem imdistanri

Step	Hyp	Ref	Expression
1		imdistanri.1	. . 3 ⊢ (φ → (ψ → χ))
2	1	com12<A> 13	. 2 ⊢ (ψ → (φ → χ))
3	2	impac 304	1 ⊢ ((ψ ∧ φ) → (χ ∧ φ))

Syntax hints:   → wi 2   ∧ wa 196

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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