Theorem ee3bir 42123

Description: Right-biconditional form of e3 42357 without virtual deduction connectives. Special theorem needed for the Virtual Deduction translation tool. (Contributed by Alan Sare, 22-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee3bir.1	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
ee3bir.2	⊢ (𝜏 ↔ 𝜃)

Assertion

Ref	Expression
ee3bir	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏)))

Proof of Theorem ee3bir

Step	Hyp	Ref	Expression
1		ee3bir.1	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
2		ee3bir.2	. . 3 ⊢ (𝜏 ↔ 𝜃)
3	2	biimpri 227	. 2 ⊢ (𝜃 → 𝜏)
4	1, 3	syl8 76	1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏)))

Syntax hints:   → wi 4   ↔ wb 205

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

This theorem is referenced by: (None)