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  1890  ssel  3220  sscon  3340  uniss  3915  trel3  4196  copsexg  4338  ssopab2  4372  coss1  4887  fununi  5400  imadif  5412  fss  5496  ssimaex  5710  opabbrex  6070  ssoprab2  6082  poxp  6402  pmss12g  6849  ss2ixp  6885  xpdom2  7020  qbtwnxr  10523  ioc0  10528  climshftlemg  11885  bezoutlembz  12598  tgcl  14817  neipsm  14907  ssnei2  14910  tgcnp  14962  cnpnei  14972  cnptopco  14975  mopni3  15237  limcresi  15419  cnlimcim  15424