Theorem anbi1ci 627

Description: Variant of anbi1i 625 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 624	. 2 ⊢ ((𝜒 ∧ 𝜑) ↔ (𝜒 ∧ 𝜓))
3	2	biancomi 464	1 ⊢ ((𝜒 ∧ 𝜑) ↔ (𝜓 ∧ 𝜒))

Syntax hints:   ↔ wb 205   ∧ wa 397

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 206  df-an 398

This theorem is referenced by:  dfid3  5578  imai  6074  frpoind  6344  wfiOLD  6353  dfac5lem3  10120  cf0  10246  eqscut2  27307  coep  34722  brtxp  34852  sscoid  34885  brapply  34910  dfrdg4  34923  wl-df4-3mintru2  36368  rnxrncnvepres  37270  rnxrnidres  37271  pmapglb  38641  polval2N  38777  rp-fakeoranass  42265  alephiso2  42309