Theorem albidOLD 2187

Description: Obsolete proof of albid 2077 as of 6-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
albidOLD.1	⊢ Ⅎ𝑥𝜑
albidOLD.2	⊢ (𝜑 → (𝜓 ↔ 𝜒))

Assertion

Ref	Expression
albidOLD	⊢ (𝜑 → (∀𝑥𝜓 ↔ ∀𝑥𝜒))

Proof of Theorem albidOLD

Step	Hyp	Ref	Expression
1		albidOLD.1	. . 3 ⊢ Ⅎ𝑥𝜑
2	1	nfriOLD 2177	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
3		albidOLD.2	. 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒))
4	2, 3	albidh 1780	1 ⊢ (𝜑 → (∀𝑥𝜓 ↔ ∀𝑥𝜒))

Syntax hints:   → wi 4   ↔ wb 195  ∀wal 1473  ℲwnfOLD 1700

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nfOLD 1712

This theorem is referenced by:  nfbidfOLD  2189