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Mirrors > Home > NFE Home > Th. List > 3simpa | GIF version |
Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994.) |
Ref | Expression |
---|---|
3simpa | ⊢ ((φ ∧ ψ ∧ χ) → (φ ∧ ψ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3an 936 | . 2 ⊢ ((φ ∧ ψ ∧ χ) ↔ ((φ ∧ ψ) ∧ χ)) | |
2 | 1 | simplbi 446 | 1 ⊢ ((φ ∧ ψ ∧ χ) → (φ ∧ ψ)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 358 ∧ w3a 934 |
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 df-3an 936 |
This theorem is referenced by: 3simpb 953 3simpc 954 simp1 955 simp2 956 3adant3 975 3adantl3 1113 3adantr3 1116 sfintfin 4532 peano4 4557 ovig 5597 ovmpt2x 5712 ce0nnulb 6182 fce 6188 |
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