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  1892  ssel  3231  sscon  3352  uniss  3934  trel3  4215  copsexg  4359  ssopab2  4393  coss1  4909  fununi  5423  imadif  5435  fss  5520  ssimaex  5737  opabbrex  6096  ssoprab2  6108  poxp  6427  pmss12g  6908  ss2ixp  6945  xpdom2  7081  qbtwnxr  10613  ioc0  10618  climshftlemg  11980  bezoutlembz  12693  tgcl  14916  neipsm  15006  ssnei2  15009  tgcnp  15061  cnpnei  15071  cnptopco  15074  mopni3  15336  limcresi  15518  cnlimcim  15523