ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3adant1l GIF version

Theorem 3adant1l 1189
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
Hypothesis
Ref Expression
3adant1l.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3adant1l (((𝜏𝜑) ∧ 𝜓𝜒) → 𝜃)

Proof of Theorem 3adant1l
StepHypRef Expression
1 3adant1l.1 . . . 4 ((𝜑𝜓𝜒) → 𝜃)
213expb 1163 . . 3 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
32adantll 465 . 2 (((𝜏𝜑) ∧ (𝜓𝜒)) → 𝜃)
433impb 1158 1 (((𝜏𝜑) ∧ 𝜓𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 943
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 945
This theorem is referenced by:  3adant2l  1191  3adant3l  1193  tfrcl  6213  addassnqg  7132  mulassnqg  7134  addasssrg  7493  axaddass  7601
  Copyright terms: Public domain W3C validator