Theorem bj-ax12iOLD 31804

Description: Old proof of bj-ax12i 31803. Obsolete as of 29-Dec-2020. (Contributed by BJ, 29-Sep-2019.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
bj-ax12i.1	⊢ (𝜑 → (𝜓 ↔ 𝜒))
bj-ax12i.2	⊢ (𝜒 → ∀𝑥𝜒)

Assertion

Ref	Expression
bj-ax12iOLD	⊢ (𝜑 → (𝜓 → ∀𝑥(𝜑 → 𝜓)))

Proof of Theorem bj-ax12iOLD

Step	Hyp	Ref	Expression
1		bj-ax12i.1	. 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒))
2		bj-ax12i.2	. . 3 ⊢ (𝜒 → ∀𝑥𝜒)
3	1	biimprcd 239	. . 3 ⊢ (𝜒 → (𝜑 → 𝜓))
4	2, 3	alrimih 1741	. 2 ⊢ (𝜒 → ∀𝑥(𝜑 → 𝜓))
5	1, 4	syl6bi 242	1 ⊢ (𝜑 → (𝜓 → ∀𝑥(𝜑 → 𝜓)))

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

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

This theorem depends on definitions:  df-bi 196

This theorem is referenced by: (None)