Theorem subbir2-P4 548

Description: Alternate Form of subbir-P3.41b 334. †

Hypotheses

Ref	Expression
subbir2-P4.1	⊢ (𝛾 → (𝜒 ↔ 𝜑))
subbir2-P4.2	⊢ (𝛾 → (𝜑 ↔ 𝜓))

Assertion

Ref	Expression
subbir2-P4	⊢ (𝛾 → (𝜒 ↔ 𝜓))

Proof of Theorem subbir2-P4

Step	Hyp	Ref	Expression
1		subbir2-P4.1	. 2 ⊢ (𝛾 → (𝜒 ↔ 𝜑))
2		subbir2-P4.2	. . . 4 ⊢ (𝛾 → (𝜑 ↔ 𝜓))
3	2	subbir-P3.41b 334	. . 3 ⊢ (𝛾 → ((𝜒 ↔ 𝜑) ↔ (𝜒 ↔ 𝜓)))
4	3	ndbief-P3.14 179	. 2 ⊢ (𝛾 → ((𝜒 ↔ 𝜑) → (𝜒 ↔ 𝜓)))
5	1, 4	ndime-P3.6 171	1 ⊢ (𝛾 → (𝜒 ↔ 𝜓))

Syntax hints:   → wff-imp 10   ↔ wff-bi 104

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-true-D2.4 155

This theorem is referenced by: (None)