Theorem biadan2OLD 814

Description: Obsolete proof of biadanii 813 as of 4-Mar-2023. (Contributed by Jeff Madsen, 20-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
biadani.1	⊢ (𝜑 → 𝜓)
biadanii.2	⊢ (𝜓 → (𝜑 ↔ 𝜒))

Assertion

Ref	Expression
biadan2OLD	⊢ (𝜑 ↔ (𝜓 ∧ 𝜒))

Proof of Theorem biadan2OLD

Step	Hyp	Ref	Expression
1		biadani.1	. . 3 ⊢ (𝜑 → 𝜓)
2	1	pm4.71ri 556	. 2 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜑))
3		biadanii.2	. . 3 ⊢ (𝜓 → (𝜑 ↔ 𝜒))
4	3	pm5.32i 570	. 2 ⊢ ((𝜓 ∧ 𝜑) ↔ (𝜓 ∧ 𝜒))
5	2, 4	bitri 267	1 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒))

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)