New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > anbi2ci | GIF version |
Description: Variant of anbi2i 675 with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) |
Ref | Expression |
---|---|
bi.aa | ⊢ (φ ↔ ψ) |
Ref | Expression |
---|---|
anbi2ci | ⊢ ((φ ∧ χ) ↔ (χ ∧ ψ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bi.aa | . . 3 ⊢ (φ ↔ ψ) | |
2 | 1 | anbi1i 676 | . 2 ⊢ ((φ ∧ χ) ↔ (ψ ∧ χ)) |
3 | ancom 437 | . 2 ⊢ ((ψ ∧ χ) ↔ (χ ∧ ψ)) | |
4 | 2, 3 | bitri 240 | 1 ⊢ ((φ ∧ χ) ↔ (χ ∧ ψ)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 176 ∧ wa 358 |
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 177 df-an 360 |
This theorem is referenced by: clabel 2475 enmap2lem1 6064 enmap1lem1 6070 lecex 6116 |
Copyright terms: Public domain | W3C validator |