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Theorem e03an 38789
Description: Conjunction form of e03 38787. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e03an.1 𝜑
e03an.2 (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜏   )
e03an.3 ((𝜑𝜏) → 𝜂)
Assertion
Ref Expression
e03an (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜂   )

Proof of Theorem e03an
StepHypRef Expression
1 e03an.1 . 2 𝜑
2 e03an.2 . 2 (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜏   )
3 e03an.3 . . 3 ((𝜑𝜏) → 𝜂)
43ex 450 . 2 (𝜑 → (𝜏𝜂))
51, 2, 4e03 38787 1 (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  (   wvd3 38623
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1038  df-vd3 38626
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator