Theorem suborr-P3.43b.RC 349

Description: Inference Form of suborr-P3.43b 348.

Hypothesis

Ref	Expression
suborr-P3.43b.RC.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
suborr-P3.43b.RC	⊢ ((𝜒 ∨ 𝜑) ↔ (𝜒 ∨ 𝜓))

Proof of Theorem suborr-P3.43b.RC

Step	Hyp	Ref	Expression
1		suborr-P3.43b.RC.1	. . . 4 ⊢ (𝜑 ↔ 𝜓)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 ↔ 𝜓))
3	2	suborr-P3.43b 348	. 2 ⊢ (⊤ → ((𝜒 ∨ 𝜑) ↔ (𝜒 ∨ 𝜓)))
4	3	ndtruee-P3.18 183	1 ⊢ ((𝜒 ∨ 𝜑) ↔ (𝜒 ∨ 𝜓))

Syntax hints:   ↔ wff-bi 104   ∨ wff-or 144  ⊤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-or-D2.3 145  df-true-D2.4 155  df-rcp-AND3 161

This theorem is referenced by:  idornthmr-P4.24b  449  oroverbi-P4.28-L3  468  lemma-L4.5  484  dfnfreealt-P6  683  nfrneg-P6  688