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Mirrors > Home > NFE Home > Th. List > 3adant1r | GIF version |
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.) |
Ref | Expression |
---|---|
3adant1l.1 | ⊢ ((φ ∧ ψ ∧ χ) → θ) |
Ref | Expression |
---|---|
3adant1r | ⊢ (((φ ∧ τ) ∧ ψ ∧ χ) → θ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3adant1l.1 | . . . 4 ⊢ ((φ ∧ ψ ∧ χ) → θ) | |
2 | 1 | 3expb 1152 | . . 3 ⊢ ((φ ∧ (ψ ∧ χ)) → θ) |
3 | 2 | adantlr 695 | . 2 ⊢ (((φ ∧ τ) ∧ (ψ ∧ χ)) → θ) |
4 | 3 | 3impb 1147 | 1 ⊢ (((φ ∧ τ) ∧ ψ ∧ χ) → θ) |
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: 3adant2r 1177 3adant3r 1179 ssfin 4470 |
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