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Theorem e1111 38720
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 6-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e1111.1 (   𝜑   ▶   𝜓   )
e1111.2 (   𝜑   ▶   𝜒   )
e1111.3 (   𝜑   ▶   𝜃   )
e1111.4 (   𝜑   ▶   𝜏   )
e1111.5 (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂))))
Assertion
Ref Expression
e1111 (   𝜑   ▶   𝜂   )

Proof of Theorem e1111
StepHypRef Expression
1 e1111.1 . . . 4 (   𝜑   ▶   𝜓   )
21in1 38607 . . 3 (𝜑𝜓)
3 e1111.2 . . . 4 (   𝜑   ▶   𝜒   )
43in1 38607 . . 3 (𝜑𝜒)
5 e1111.3 . . . 4 (   𝜑   ▶   𝜃   )
65in1 38607 . . 3 (𝜑𝜃)
7 e1111.4 . . . 4 (   𝜑   ▶   𝜏   )
87in1 38607 . . 3 (𝜑𝜏)
9 e1111.5 . . 3 (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂))))
102, 4, 6, 8, 9ee1111 38542 . 2 (𝜑𝜂)
1110dfvd1ir 38609 1 (   𝜑   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 38605
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-vd1 38606
This theorem is referenced by:  trsbcVD  38933
  Copyright terms: Public domain W3C validator