Theorem anbi1ci 637

Description: Variant of anbi1i 635 with commutation. (Contributed by Peter Mazsa, 7-Mar-2020.)

Hypothesis

Ref	Expression
anbi.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
anbi1ci	⊢ ((𝜒 ∧ 𝜑) ↔ (𝜓 ∧ 𝜒))

Proof of Theorem anbi1ci

Step	Hyp	Ref	Expression
1		anbi.1	. . 3 ⊢ (𝜑 ↔ 𝜓)
2	1	anbi2i 634	. 2 ⊢ ((𝜒 ∧ 𝜑) ↔ (𝜒 ∧ 𝜓))
3	2	biancomi 467	1 ⊢ ((𝜒 ∧ 𝜑) ↔ (𝜓 ∧ 𝜒))

Syntax hints:   ↔ wb 209   ∧ wa 400

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 210  df-an 401

This theorem is referenced by:  dfid3  5561  imai  6078  frpoind  6345  dfac5lem3  10110  cf0  10235  eqcuts2  27960  coep  36225  brtxp  36351  sscoid  36384  brapply  36409  dfrdg4  36424  wl-df4-3mintru2  38114  rnxrncnvepres  39053  rnxrnidres  39054  pmapglb  40525  polval2N  40661  rp-fakeoranass  44223  alephiso2  44267