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Theorem bitr3VD 37909
Description: Virtual deduction proof of bitr3 340. The following user's proof is completed by invoking mmj2's unify command and using mmj2's StepSelector to pick all remaining steps of the Metamath proof.
1:: (   (𝜑𝜓)   ▶   (𝜑 𝜓)   )
2:1,?: e1a 37676 (   (𝜑𝜓)   ▶   (𝜓 𝜑)   )
3:: (   (𝜑𝜓)   ,   (𝜑𝜒)    ▶   (𝜑𝜒)   )
4:3,?: e2 37680 (   (𝜑𝜓)   ,   (𝜑𝜒)    ▶   (𝜒𝜑)   )
5:2,4,?: e12 37775 (   (𝜑𝜓)   ,   (𝜑𝜒)    ▶   (𝜓𝜒)   )
6:5: (   (𝜑𝜓)   ▶   ((𝜑 𝜒) → (𝜓𝜒))   )
qed:6: ((𝜑𝜓) → ((𝜑𝜒) → (𝜓𝜒)))
(Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
bitr3VD ((𝜑𝜓) → ((𝜑𝜒) → (𝜓𝜒)))

Proof of Theorem bitr3VD
StepHypRef Expression
1 id 22 . . 3 ((𝜑𝜓) → (𝜑𝜓))
21bicomd 211 . 2 ((𝜑𝜓) → (𝜓𝜑))
3 id 22 . . 3 ((𝜑𝜒) → (𝜑𝜒))
43bicomd 211 . 2 ((𝜑𝜒) → (𝜒𝜑))
5 biantr 967 . . 3 (((𝜓𝜑) ∧ (𝜒𝜑)) → (𝜓𝜒))
65ex 448 . 2 ((𝜓𝜑) → ((𝜒𝜑) → (𝜓𝜒)))
72, 4, 6syl2im 39 1 ((𝜑𝜓) → ((𝜑𝜒) → (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194
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 195  df-an 384
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator