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Mirrors > Home > MPE Home > Th. List > anbi1ci | Structured version Visualization version GIF version |
Description: Variant of anbi1i 624 with commutation. (Contributed by Peter Mazsa, 7-Mar-2020.) |
Ref | Expression |
---|---|
anbi.1 | ⊢ (𝜑 ↔ 𝜓) |
Ref | Expression |
---|---|
anbi1ci | ⊢ ((𝜒 ∧ 𝜑) ↔ (𝜓 ∧ 𝜒)) |
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)) |
Colors of variables: wff setvar class |
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 5586 imai 6094 frpoind 6365 wfiOLD 6374 dfac5lem3 10163 cf0 10289 eqscut2 27866 coep 35732 brtxp 35862 sscoid 35895 brapply 35920 dfrdg4 35933 wl-df4-3mintru2 37470 rnxrncnvepres 38382 rnxrnidres 38383 pmapglb 39753 polval2N 39889 rp-fakeoranass 43504 alephiso2 43548 |
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