Theorem anbi1ci 626

Description: Variant of anbi1i 624 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 623	. 2 ⊢ ((𝜒 ∧ 𝜑) ↔ (𝜒 ∧ 𝜓))
3	2	biancomi 462	1 ⊢ ((𝜒 ∧ 𝜑) ↔ (𝜓 ∧ 𝜒))

Syntax hints:   ↔ wb 206   ∧ wa 395

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 207  df-an 396

This theorem is referenced by:  dfid3  5539  imai  6048  frpoind  6318  dfac5lem3  10085  cf0  10211  eqscut2  27725  coep  35746  brtxp  35875  sscoid  35908  brapply  35933  dfrdg4  35946  wl-df4-3mintru2  37482  rnxrncnvepres  38393  rnxrnidres  38394  pmapglb  39771  polval2N  39907  rp-fakeoranass  43510  alephiso2  43554