Theorem acco 43

Description: & is commutative.

Hypothesis

Ref	Expression
acco.1	⊦ (𝜑 ⅋ (𝜓 & 𝜒))

Assertion

Ref	Expression
acco	⊦ (𝜑 ⅋ (𝜒 & 𝜓))

Proof of Theorem acco

Step	Hyp	Ref	Expression
1		acco.1	. . 3 ⊦ (𝜑 ⅋ (𝜓 & 𝜒))
2	1	eac2d 39	. 2 ⊦ (𝜑 ⅋ 𝜒)
3	1	eac1d 37	. 2 ⊦ (𝜑 ⅋ 𝜓)
4	2, 3	iac 35	1 ⊦ (𝜑 ⅋ (𝜒 & 𝜓))

Syntax hints:   ⅋ wmd 2   & wac 30

This theorem was proved from axioms:  ax-ibot 4  ax-ebot 5  ax-cut 6  ax-init 7  ax-mdco 8  ax-iac 32  ax-eac1 33  ax-eac2 34

This theorem is referenced by:  acm2  81