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Mirrors > Home > ILE Home > Th. List > 3com13 | GIF version |
Description: Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.) |
Ref | Expression |
---|---|
3exp.1 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
3com13 | ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3anrev 929 | . 2 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) ↔ (𝜑 ∧ 𝜓 ∧ 𝜒)) | |
2 | 3exp.1 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
3 | 1, 2 | sylbi 119 | 1 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) → 𝜃) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ w3a 919 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 df-3an 921 |
This theorem is referenced by: 3coml 1145 3adant3l 1165 3adant3r 1166 syld3an1 1215 oaword1 6073 nnacan 6108 subadd 7311 xrltso 8871 iooshf 8975 dvdsmulc 10223 lcmdvdsb 10466 |
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