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Mirrors > Home > ILE Home > Th. List > 3adant2r | 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 |
---|---|
3adant2r | ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜏) ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3adant1l.1 | . . . 4 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
2 | 1 | 3com12 1196 | . . 3 ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜒) → 𝜃) |
3 | 2 | 3adant1r 1220 | . 2 ⊢ (((𝜓 ∧ 𝜏) ∧ 𝜑 ∧ 𝜒) → 𝜃) |
4 | 3 | 3com12 1196 | 1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜏) ∧ 𝜒) → 𝜃) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 ∧ w3a 967 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-3an 969 |
This theorem is referenced by: caovimo 6027 mulassnqg 7317 prarloc 7436 ltexprlemfl 7542 ltexprlemfu 7544 addasssrg 7689 axaddass 7805 |
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