Theorem anim2d 337

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 335	1 ⊢ (𝜑 → ((𝜃 ∧ 𝜓) → (𝜃 ∧ 𝜒)))

Syntax hints:   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  spsbim  1843  ssel  3149  sscon  3269  uniss  3830  trel3  4109  copsexg  4244  ssopab2  4275  coss1  4782  fununi  5284  imadif  5296  fss  5377  ssimaex  5577  opabbrex  5918  ssoprab2  5930  poxp  6232  pmss12g  6674  ss2ixp  6710  xpdom2  6830  qbtwnxr  10255  ioc0  10260  climshftlemg  11305  bezoutlembz  11999  tgcl  13457  neipsm  13547  ssnei2  13550  tgcnp  13602  cnpnei  13612  cnptopco  13615  mopni3  13877  limcresi  14028  cnlimcim  14033