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Theorem simplbi2VD 37980
Description: Virtual deduction proof of simplbi2 652. 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 37897 ((𝜓𝜒) → 𝜑)
qed:3,?: e0a 37897 (𝜓 → (𝜒𝜑))
The proof of simplbi2 652 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 208 . . 3 ((𝜑 ↔ (𝜓𝜒)) → ((𝜓𝜒) → 𝜑))
31, 2e0a 37897 . 2 ((𝜓𝜒) → 𝜑)
4 pm3.3 458 . 2 (((𝜓𝜒) → 𝜑) → (𝜓 → (𝜒𝜑)))
53, 4e0a 37897 1 (𝜓 → (𝜒𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  wa 382
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