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  3151  sscon  3271  uniss  3832  trel3  4111  copsexg  4246  ssopab2  4277  coss1  4784  fununi  5286  imadif  5298  fss  5379  ssimaex  5579  opabbrex  5921  ssoprab2  5933  poxp  6235  pmss12g  6677  ss2ixp  6713  xpdom2  6833  qbtwnxr  10260  ioc0  10265  climshftlemg  11312  bezoutlembz  12007  tgcl  13603  neipsm  13693  ssnei2  13696  tgcnp  13748  cnpnei  13758  cnptopco  13761  mopni3  14023  limcresi  14174  cnlimcim  14179