Theorem anim2d 548

Description: Add a conjunct to left of antecedent and consequent in a deduction. (Contributed by NM, 5-Aug-1993.)

Hypothesis

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

Assertion

Ref	Expression
anim2d	⊢ (φ → ((θ ∧ ψ) → (θ ∧ χ)))

Proof of Theorem anim2d

Step	Hyp	Ref	Expression
1		idd 21	. 2 ⊢ (φ → (θ → θ))
2		anim1d.1	. 2 ⊢ (φ → (ψ → χ))
3	1, 2	anim12d 546	1 ⊢ (φ → ((θ ∧ ψ) → (θ ∧ 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:  moeq3  3014  ssel  3268  sscon  3401  uniss  3913  copsexg  4608  ssopab2  4713  coss1  4873  fununi  5161  imadif  5172  fss  5231  weds  5939