Theorem simplbi2VD 38103

Description: Virtual deduction proof of simplbi2 653. 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 38020	⊢ ((𝜓 ∧ 𝜒) → 𝜑)
qed:3,?: e0a 38020	⊢ (𝜓 → (𝜒 → 𝜑))

The proof of simplbi2 653 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 209	. . 3 ⊢ ((𝜑 ↔ (𝜓 ∧ 𝜒)) → ((𝜓 ∧ 𝜒) → 𝜑))
3	1, 2	e0a 38020	. 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜑)
4		pm3.3 459	. 2 ⊢ (((𝜓 ∧ 𝜒) → 𝜑) → (𝜓 → (𝜒 → 𝜑)))
5	3, 4	e0a 38020	1 ⊢ (𝜓 → (𝜒 → 𝜑))

Syntax hints:   → wi 4   ↔ wb 195   ∧ 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 196  df-an 385

This theorem is referenced by: (None)