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  3287  ssrexv  3290  ssdif  3340  ssrin  3430  reupick  3489  disjss1  4068  copsexg  4334  po3nr  4405  coss2  4884  fununi  5395  fiintim  7118  recexprlemlol  7839  recexprlemupu  7841  icoshft  10218  2ffzeq  10369  qbtwnxr  10510  ico0  10514  r19.2uz  11547  bezoutlemzz  12566  bezoutlemaz  12567  ptex  13340  rnglidlmmgm  14503  neiss  14867  uptx  14991  txcn  14992  bj-charfundcALT  16354