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  1854  ssel  3173  sscon  3293  uniss  3856  trel3  4135  copsexg  4273  ssopab2  4306  coss1  4817  fununi  5322  imadif  5334  fss  5415  ssimaex  5618  opabbrex  5962  ssoprab2  5974  poxp  6285  pmss12g  6729  ss2ixp  6765  xpdom2  6885  qbtwnxr  10326  ioc0  10331  climshftlemg  11445  bezoutlembz  12141  tgcl  14232  neipsm  14322  ssnei2  14325  tgcnp  14377  cnpnei  14387  cnptopco  14390  mopni3  14652  limcresi  14820  cnlimcim  14825