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Theorem e33an 39279
Description: Conjunction form of e33 39278. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e33an.1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
e33an.2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )
e33an.3 ((𝜃𝜏) → 𝜂)
Assertion
Ref Expression
e33an (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜂   )

Proof of Theorem e33an
StepHypRef Expression
1 e33an.1 . 2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
2 e33an.2 . 2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )
3 e33an.3 . . 3 ((𝜃𝜏) → 𝜂)
43ex 449 . 2 (𝜃 → (𝜏𝜂))
51, 2, 4e33 39278 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  (   wvd3 39120
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 385  df-3an 1056  df-vd3 39123
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator