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Mirrors > Home > ILE Home > Th. List > ancomd | GIF version |
Description: Commutation of conjuncts in consequent. (Contributed by Jeff Hankins, 14-Aug-2009.) |
Ref | Expression |
---|---|
ancomd.1 | ⊢ (𝜑 → (𝜓 ∧ 𝜒)) |
Ref | Expression |
---|---|
ancomd | ⊢ (𝜑 → (𝜒 ∧ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancomd.1 | . 2 ⊢ (𝜑 → (𝜓 ∧ 𝜒)) | |
2 | ancom 253 | . 2 ⊢ ((𝜓 ∧ 𝜒) ↔ (𝜒 ∧ 𝜓)) | |
3 | 1, 2 | sylib 127 | 1 ⊢ (𝜑 → (𝜒 ∧ 𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: elres 4646 relbrcnvg 4704 fvelrnb 5221 relelec 6146 prcdnql 6582 1idpru 6689 gt0srpr 6833 |
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