Theorem anim1d 336

Description: Add a conjunct to right of antecedent and consequent in a deduction. (Contributed by NM, 3-Apr-1994.)

Hypothesis

Ref	Expression
anim1d.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
anim1d	⊢ (𝜑 → ((𝜓 ∧ 𝜃) → (𝜒 ∧ 𝜃)))

Proof of Theorem anim1d

Step	Hyp	Ref	Expression
1		anim1d.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		idd 21	. 2 ⊢ (𝜑 → (𝜃 → 𝜃))
3	1, 2	anim12d 335	1 ⊢ (𝜑 → ((𝜓 ∧ 𝜃) → (𝜒 ∧ 𝜃)))

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:  pm3.45  599  exdistrfor  1846  mopick2  2161  ssrexf  3286  ssrexv  3289  ssdif  3339  ssrin  3429  reupick  3488  disjss1  4064  copsexg  4329  po3nr  4398  coss2  4875  fununi  5385  fiintim  7081  recexprlemlol  7801  recexprlemupu  7803  icoshft  10174  2ffzeq  10325  qbtwnxr  10464  ico0  10468  r19.2uz  11490  bezoutlemzz  12509  bezoutlemaz  12510  ptex  13283  rnglidlmmgm  14445  neiss  14809  uptx  14933  txcn  14934  bj-charfundcALT  16102