Theorem suborl-P3.43a.RC 347

Description: Inference Form of suborl-P3.43a 346. †

Hypothesis

Ref	Expression
suborl-P3.43a.RC.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
suborl-P3.43a.RC	⊢ ((𝜑 ∨ 𝜒) ↔ (𝜓 ∨ 𝜒))

Proof of Theorem suborl-P3.43a.RC

Step	Hyp	Ref	Expression
1		suborl-P3.43a.RC.1	. . . 4 ⊢ (𝜑 ↔ 𝜓)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 ↔ 𝜓))
3	2	suborl-P3.43a 346	. 2 ⊢ (⊤ → ((𝜑 ∨ 𝜒) ↔ (𝜓 ∨ 𝜒)))
4	3	ndtruee-P3.18 183	1 ⊢ ((𝜑 ∨ 𝜒) ↔ (𝜓 ∨ 𝜒))

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:  idornthml-P4.24a  448  oroverim-P4.28-L1  465  dfnfree-P7  968  dfnfreeint-P7  969