Theorem subandr2-P4.RC 555

Description: Inference Form of subandr2-P4 554. †

Hypotheses

Ref	Expression
subandr2-P4.RC.1	⊢ (𝜒 ∧ 𝜑)
subandr2-P4.RC.2	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
subandr2-P4.RC	⊢ (𝜒 ∧ 𝜓)

Proof of Theorem subandr2-P4.RC

Step	Hyp	Ref	Expression
1		subandr2-P4.RC.1	. . . 4 ⊢ (𝜒 ∧ 𝜑)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜒 ∧ 𝜑))
3		subandr2-P4.RC.2	. . . 4 ⊢ (𝜑 ↔ 𝜓)
4	3	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 ↔ 𝜓))
5	2, 4	subandr2-P4 554	. 2 ⊢ (⊤ → (𝜒 ∧ 𝜓))
6	5	ndtruee-P3.18 183	1 ⊢ (𝜒 ∧ 𝜓)

Syntax hints:   ↔ wff-bi 104   ∧ wff-and 132  ⊤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: (None)