Theorem simplbi2VD 42355

Description: Virtual deduction proof of simplbi2 500. 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 42281	⊢ ((𝜓 ∧ 𝜒) → 𝜑)
qed:3,?: e0a 42281	⊢ (𝜓 → (𝜒 → 𝜑))

The proof of simplbi2 500 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 ↔ (𝜓 ∧ 𝜒))

Assertion

Ref	Expression
simplbi2VD	⊢ (𝜓 → (𝜒 → 𝜑))

Proof of Theorem simplbi2VD

Step	Hyp	Ref	Expression
1		pm3.26bi2VD.1	. . 3 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒))
2		biimpr 219	. . 3 ⊢ ((𝜑 ↔ (𝜓 ∧ 𝜒)) → ((𝜓 ∧ 𝜒) → 𝜑))
3	1, 2	e0a 42281	. 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜑)
4		pm3.3 448	. 2 ⊢ (((𝜓 ∧ 𝜒) → 𝜑) → (𝜓 → (𝜒 → 𝜑)))
5	3, 4	e0a 42281	1 ⊢ (𝜓 → (𝜒 → 𝜑))

Syntax hints:   → wi 4   ↔ wb 205   ∧ wa 395

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 206  df-an 396

This theorem is referenced by: (None)