Theorem bitrns-P3.33c.CL 304

Description: Closed Form of bitrns-P3.33c 302.

Assertion

Ref	Expression
bitrns-P3.33c.CL	⊢ (((𝜑 ↔ 𝜓) ∧ (𝜓 ↔ 𝜒)) → (𝜑 ↔ 𝜒))

Proof of Theorem bitrns-P3.33c.CL

Step	Hyp	Ref	Expression
1		rcp-NDASM1of2 193	. 2 ⊢ (((𝜑 ↔ 𝜓) ∧ (𝜓 ↔ 𝜒)) → (𝜑 ↔ 𝜓))
2		rcp-NDASM2of2 194	. 2 ⊢ (((𝜑 ↔ 𝜓) ∧ (𝜓 ↔ 𝜒)) → (𝜓 ↔ 𝜒))
3	1, 2	bitrns-P3.33c 302	1 ⊢ (((𝜑 ↔ 𝜓) ∧ (𝜓 ↔ 𝜒)) → (𝜑 ↔ 𝜒))

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:  trnsvsubw-P6  710  trnsvsub-P6  763