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  1857  ssel  3177  sscon  3297  uniss  3860  trel3  4139  copsexg  4277  ssopab2  4310  coss1  4821  fununi  5326  imadif  5338  fss  5419  ssimaex  5622  opabbrex  5966  ssoprab2  5978  poxp  6290  pmss12g  6734  ss2ixp  6770  xpdom2  6890  qbtwnxr  10347  ioc0  10352  climshftlemg  11467  bezoutlembz  12171  tgcl  14300  neipsm  14390  ssnei2  14393  tgcnp  14445  cnpnei  14455  cnptopco  14458  mopni3  14720  limcresi  14902  cnlimcim  14907