Theorem andcomm2-P4 564

Description: Alternate Form of andcomm-P3.35 314. †

Hypothesis

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

Assertion

Ref	Expression
andcomm2-P4	⊢ (𝛾 → (𝜓 ∧ 𝜑))

Proof of Theorem andcomm2-P4

Step	Hyp	Ref	Expression
1		andcomm2-P4.1	. 2 ⊢ (𝛾 → (𝜑 ∧ 𝜓))
2		andcomm-P3.35 314	. . 3 ⊢ ((𝜑 ∧ 𝜓) ↔ (𝜓 ∧ 𝜑))
3	2	rcp-NDIMP0addall 207	. 2 ⊢ (𝛾 → ((𝜑 ∧ 𝜓) ↔ (𝜓 ∧ 𝜑)))
4	1, 3	bimpf-P4 531	1 ⊢ (𝛾 → (𝜓 ∧ 𝜑))

Syntax hints:   → wff-imp 10   ↔ wff-bi 104   ∧ wff-and 132

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:  andcomm2-P4.RC  565