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  597  exdistrfor  1798  mopick2  2107  ssrexf  3215  ssrexv  3218  ssdif  3268  ssrin  3358  reupick  3417  disjss1  3981  copsexg  4238  po3nr  4304  coss2  4776  fununi  5276  fiintim  6918  recexprlemlol  7600  recexprlemupu  7602  icoshft  9959  2ffzeq  10109  qbtwnxr  10226  ico0  10230  r19.2uz  10968  bezoutlemzz  11968  bezoutlemaz  11969  neiss  13201  uptx  13325  txcn  13326  bj-charfundcALT  14101