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  3218  sscon  3338  uniss  3909  trel3  4190  copsexg  4331  ssopab2  4365  coss1  4880  fununi  5392  imadif  5404  fss  5488  ssimaex  5700  opabbrex  6057  ssoprab2  6069  poxp  6389  pmss12g  6835  ss2ixp  6871  xpdom2  7003  qbtwnxr  10494  ioc0  10499  climshftlemg  11834  bezoutlembz  12546  tgcl  14759  neipsm  14849  ssnei2  14852  tgcnp  14904  cnpnei  14914  cnptopco  14917  mopni3  15179  limcresi  15361  cnlimcim  15366