Theorem andcomm2-P4.RC 565

Description: Inference Form of andcomm2-P4 564. †

Hypothesis

Ref	Expression
andcomm2-P4.RC.1	⊢ (𝜑 ∧ 𝜓)

Assertion

Ref	Expression
andcomm2-P4.RC	⊢ (𝜓 ∧ 𝜑)

Proof of Theorem andcomm2-P4.RC

Step	Hyp	Ref	Expression
1		andcomm2-P4.RC.1	. . . 4 ⊢ (𝜑 ∧ 𝜓)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 ∧ 𝜓))
3	2	andcomm2-P4 564	. 2 ⊢ (⊤ → (𝜓 ∧ 𝜑))
4	3	ndtruee-P3.18 183	1 ⊢ (𝜓 ∧ 𝜑)

Syntax hints:   ∧ 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)