Theorem imdistani 671

Description: Distribution of implication with conjunction. (Contributed by NM, 1-Aug-1994.)

Hypothesis

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

Assertion

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

Proof of Theorem imdistani

Step	Hyp	Ref	Expression
1		imdistani.1	. . 3 ⊢ (φ → (ψ → χ))
2	1	anc2li 540	. 2 ⊢ (φ → (ψ → (φ ∧ χ)))
3	2	imp 418	1 ⊢ ((φ ∧ ψ) → (φ ∧ χ))

Syntax hints:   → wi 4   ∧ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  nfan1  1881  2eu1  2284  difrab  3530  foconst  5281  dffo4  5424  dffo5  5425