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

Theorem alanimi 1364
Description: Variant of al2imi 1363 with conjunctive antecedent. (Contributed by Andrew Salmon, 8-Jun-2011.)
Hypothesis
Ref Expression
alanimi.1 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
alanimi ((∀𝑥𝜑 ∧ ∀𝑥𝜓) → ∀𝑥𝜒)

Proof of Theorem alanimi
StepHypRef Expression
1 alanimi.1 . . . 4 ((𝜑𝜓) → 𝜒)
21ex 112 . . 3 (𝜑 → (𝜓𝜒))
32al2imi 1363 . 2 (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
43imp 119 1 ((∀𝑥𝜑 ∧ ∀𝑥𝜓) → ∀𝑥𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wal 1257
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354
This theorem is referenced by:  19.26  1386  alsyl  1542  vtoclgft  2621  euind  2751  reuind  2767  sbeqalb  2842  bm1.3ii  3906  trin2  4744  bdbm1.3ii  10398
  Copyright terms: Public domain W3C validator