Theorem mccob 116

Description: ⊗ is commutative. Biconditional version of mcco 115.

Assertion

Ref	Expression
mccob	⊦ ((𝜑 ⊗ 𝜓) ⧟ (𝜓 ⊗ 𝜑))

Proof of Theorem mccob

Step	Hyp	Ref	Expression
1		mcco 115	. 2 ⊦ ((𝜑 ⊗ 𝜓) ⊸ (𝜓 ⊗ 𝜑))
2		mcco 115	. 2 ⊦ ((𝜓 ⊗ 𝜑) ⊸ (𝜑 ⊗ 𝜓))
3	1, 2	ilb 96	1 ⊦ ((𝜑 ⊗ 𝜓) ⧟ (𝜓 ⊗ 𝜑))

Syntax hints:   ⧟ wlb 55   ⊗ wmc 105

This theorem was proved from axioms:  ax-ibot 4  ax-ebot 5  ax-cut 6  ax-init 7  ax-mdco 8  ax-mdas 9  ax-iac 32  ax-eac1 33  ax-eac2 34

This theorem depends on definitions:  df-lb 56  df-li 62  df-mc 106

This theorem is referenced by: (None)