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Theorem simplbi2VD 39395
Description: Virtual deduction proof of simplbi2 654. 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.
h1:: (𝜑 ↔ (𝜓𝜒))
3:1,?: e0a 39316 ((𝜓𝜒) → 𝜑)
qed:3,?: e0a 39316 (𝜓 → (𝜒𝜑))
The proof of simplbi2 654 was automatically derived from it. (Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
pm3.26bi2VD.1 (𝜑 ↔ (𝜓𝜒))
Assertion
Ref Expression
simplbi2VD (𝜓 → (𝜒𝜑))

Proof of Theorem simplbi2VD
StepHypRef Expression
1 pm3.26bi2VD.1 . . 3 (𝜑 ↔ (𝜓𝜒))
2 biimpr 210 . . 3 ((𝜑 ↔ (𝜓𝜒)) → ((𝜓𝜒) → 𝜑))
31, 2e0a 39316 . 2 ((𝜓𝜒) → 𝜑)
4 pm3.3 459 . 2 (((𝜓𝜒) → 𝜑) → (𝜓 → (𝜒𝜑)))
53, 4e0a 39316 1 (𝜓 → (𝜒𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 383
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
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator