Theorem subbil2-P4 546

Description: Alternate Form of subbil-P3.41a 332. †

Hypotheses

Ref	Expression
subbil2-P4.1	⊢ (𝛾 → (𝜑 ↔ 𝜒))
subbil2-P4.2	⊢ (𝛾 → (𝜑 ↔ 𝜓))

Assertion

Ref	Expression
subbil2-P4	⊢ (𝛾 → (𝜓 ↔ 𝜒))

Proof of Theorem subbil2-P4

Step	Hyp	Ref	Expression
1		subbil2-P4.1	. 2 ⊢ (𝛾 → (𝜑 ↔ 𝜒))
2		subbil2-P4.2	. . . 4 ⊢ (𝛾 → (𝜑 ↔ 𝜓))
3	2	subbil-P3.41a 332	. . 3 ⊢ (𝛾 → ((𝜑 ↔ 𝜒) ↔ (𝜓 ↔ 𝜒)))
4	3	ndbief-P3.14 179	. 2 ⊢ (𝛾 → ((𝜑 ↔ 𝜒) → (𝜓 ↔ 𝜒)))
5	1, 4	ndime-P3.6 171	1 ⊢ (𝛾 → (𝜓 ↔ 𝜒))

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

This theorem is referenced by:  subbil2-P4.RC  547