Theorem bisym-P2.6b 124

Description: Equivalence Property: '↔' Symmetry.

Assertion

Ref	Expression
bisym-P2.6b	⊢ ((𝜑 ↔ 𝜓) → (𝜓 ↔ 𝜑))

Proof of Theorem bisym-P2.6b

Step	Hyp	Ref	Expression
1		birev-P2.5b 115	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜓 → 𝜑))
2		bifwd-P2.5a 111	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 → 𝜓))
3	1, 2	bicmb-P2.5c.AC.2SH 121	1 ⊢ ((𝜑 ↔ 𝜓) → (𝜓 ↔ 𝜑))

Syntax hints:   → wff-imp 10   ↔ wff-bi 104

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

This theorem is referenced by:  bisym-P2.6b.SH  125