Theorem subbir-P3.41b.RC 335

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

Hypothesis

Ref	Expression
subbir-P3.41b.RC.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
subbir-P3.41b.RC	⊢ ((𝜒 ↔ 𝜑) ↔ (𝜒 ↔ 𝜓))

Proof of Theorem subbir-P3.41b.RC

Step	Hyp	Ref	Expression
1		subbir-P3.41b.RC.1	. . . 4 ⊢ (𝜑 ↔ 𝜓)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 ↔ 𝜓))
3	2	subbir-P3.41b 334	. 2 ⊢ (⊤ → ((𝜒 ↔ 𝜑) ↔ (𝜒 ↔ 𝜓)))
4	3	ndtruee-P3.18 183	1 ⊢ ((𝜒 ↔ 𝜑) ↔ (𝜒 ↔ 𝜓))

Syntax hints:   ↔ wff-bi 104  ⊤wff-true 153

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:  solvesub-P6b  707  solvedsub-P6b  713  psubtoisubv-P6  725  psubtoisub-P6  765