Theorem anbi1ci 628

Description: Variant of anbi1i 626 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 625	. 2 ⊢ ((𝜒 ∧ 𝜑) ↔ (𝜒 ∧ 𝜓))
3	2	biancomi 466	1 ⊢ ((𝜒 ∧ 𝜑) ↔ (𝜓 ∧ 𝜒))

Syntax hints:   ↔ wb 209   ∧ wa 399

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 400

This theorem is referenced by:  dfid3  5427  imai  5909  wfi  6149  dfac5lem3  9536  cf0  9662  coep  33100  frpoind  33193  brtxp  33454  sscoid  33487  brapply  33512  dfrdg4  33525  wl-df4-3mintru2  34904  rnxrncnvepres  35808  rnxrnidres  35809  pmapglb  37066  polval2N  37202  rp-fakeoranass  40222  alephiso2  40257