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Theorem simplbi2VD 40015
Description: Virtual deduction proof of simplbi2 496. 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 ↔ (𝜓 ∧ 𝜒)) 3:1,?: e0a 39941 ⊢ ((𝜓 ∧ 𝜒) → 𝜑) qed:3,?: e0a 39941 ⊢ (𝜓 → (𝜒 → 𝜑))
The proof of simplbi2 496 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 212 . . 3 ((𝜑 ↔ (𝜓𝜒)) → ((𝜓𝜒) → 𝜑))
31, 2e0a 39941 . 2 ((𝜓𝜒) → 𝜑)
4 pm3.3 441 . 2 (((𝜓𝜒) → 𝜑) → (𝜓 → (𝜒𝜑)))
53, 4e0a 39941 1 (𝜓 → (𝜒𝜑))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 198   ∧ wa 386 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 199  df-an 387 This theorem is referenced by: (None)
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