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  1889  ssel  3219  sscon  3339  uniss  3912  trel3  4193  copsexg  4334  ssopab2  4368  coss1  4883  fununi  5395  imadif  5407  fss  5491  ssimaex  5703  opabbrex  6060  ssoprab2  6072  poxp  6392  pmss12g  6839  ss2ixp  6875  xpdom2  7010  qbtwnxr  10510  ioc0  10515  climshftlemg  11856  bezoutlembz  12568  tgcl  14781  neipsm  14871  ssnei2  14874  tgcnp  14926  cnpnei  14936  cnptopco  14939  mopni3  15201  limcresi  15383  cnlimcim  15388