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  1891  ssel  3221  sscon  3341  uniss  3914  trel3  4195  copsexg  4336  ssopab2  4370  coss1  4885  fununi  5398  imadif  5410  fss  5494  ssimaex  5707  opabbrex  6065  ssoprab2  6077  poxp  6397  pmss12g  6844  ss2ixp  6880  xpdom2  7015  qbtwnxr  10518  ioc0  10523  climshftlemg  11864  bezoutlembz  12577  tgcl  14791  neipsm  14881  ssnei2  14884  tgcnp  14936  cnpnei  14946  cnptopco  14949  mopni3  15211  limcresi  15393  cnlimcim  15398