Theorem anbi1ci 632

Description: Variant of anbi1i 630 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 629	. 2 ⊢ ((𝜒 ∧ 𝜑) ↔ (𝜒 ∧ 𝜓))
3	2	biancomi 463	1 ⊢ ((𝜒 ∧ 𝜑) ↔ (𝜓 ∧ 𝜒))

Syntax hints:   ↔ wb 207   ∧ wa 396

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 208  df-an 397

This theorem is referenced by:  dfid3  5516  imai  6026  frpoind  6293  dfac5lem3  10038  cf0  10164  eqcuts2  27796  coep  35980  brtxp  36106  sscoid  36139  brapply  36164  dfrdg4  36179  wl-df4-3mintru2  37849  rnxrncnvepres  38790  rnxrnidres  38791  pmapglb  40262  polval2N  40398  rp-fakeoranass  43958  alephiso2  44002