Theorem anim1d 547

Description: Add a conjunct to right of antecedent and consequent in a deduction. (Contributed by NM, 3-Apr-1994.)

Hypothesis

Ref	Expression
anim1d.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
anim1d	⊢ (φ → ((ψ ∧ θ) → (χ ∧ θ)))

Proof of Theorem anim1d

Step	Hyp	Ref	Expression
1		anim1d.1	. 2 ⊢ (φ → (ψ → χ))
2		idd 21	. 2 ⊢ (φ → (θ → θ))
3	1, 2	anim12d 546	1 ⊢ (φ → ((ψ ∧ θ) → (χ ∧ θ)))

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:  pm3.45  807  ax12olem2  1928  exdistrf  1971  mopick2  2271  ssrexv  3331  ssdif  3401  ssrin  3480  reupick  3539  copsexg  4607  coss2  4873  fununi  5160  fnfreclem3  6319