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  4330  ssopab2  4364  coss1  4877  fununi  5389  imadif  5401  fss  5485  ssimaex  5697  opabbrex  6054  ssoprab2  6066  poxp  6384  pmss12g  6830  ss2ixp  6866  xpdom2  6998  qbtwnxr  10485  ioc0  10490  climshftlemg  11821  bezoutlembz  12533  tgcl  14746  neipsm  14836  ssnei2  14839  tgcnp  14891  cnpnei  14901  cnptopco  14904  mopni3  15166  limcresi  15348  cnlimcim  15353