ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3adant3r GIF version

Theorem 3adant3r 1235
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
Hypothesis
Ref Expression
3adant1l.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3adant3r ((𝜑𝜓 ∧ (𝜒𝜏)) → 𝜃)

Proof of Theorem 3adant3r
StepHypRef Expression
1 3adant1l.1 . . . 4 ((𝜑𝜓𝜒) → 𝜃)
213com13 1208 . . 3 ((𝜒𝜓𝜑) → 𝜃)
323adant1r 1231 . 2 (((𝜒𝜏) ∧ 𝜓𝜑) → 𝜃)
433com13 1208 1 ((𝜑𝜓 ∧ (𝜒𝜏)) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  w3a 978
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  df-3an 980
This theorem is referenced by:  addassnqg  7380  mulassnqg  7382  prarloc  7501  ltpopr  7593  ltexprlemfl  7607  ltexprlemfu  7609  addasssrg  7754  axaddass  7870  apmul1  8743  ltmul2  8811  lemul2  8812  dvdscmulr  11822  dvdsmulcr  11823  modremain  11928  ndvdsadd  11930  rpexp12i  12149  xblcntrps  13806  xblcntr  13807
  Copyright terms: Public domain W3C validator