Theorem biancom 33994

Description: Commuting conjunction in a biconditional. (Contributed by Peter Mazsa, 17-Jun-2018.)

Hypothesis

Ref	Expression
biancom.1	⊢ (𝜑 ↔ (𝜒 ∧ 𝜓))

Assertion

Ref	Expression
biancom	⊢ (𝜑 ↔ (𝜓 ∧ 𝜒))

Proof of Theorem biancom

Step	Hyp	Ref	Expression
1		biancom.1	. 2 ⊢ (𝜑 ↔ (𝜒 ∧ 𝜓))
2		ancom 466	. 2 ⊢ ((𝜓 ∧ 𝜒) ↔ (𝜒 ∧ 𝜓))
3	1, 2	bitr4i 267	1 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒))

Syntax hints:   ↔ wb 196   ∧ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  anbi1ci  33996  rabeqel  34019  iss2  34112